1,0,0,0,0.000000," ","integrate(asinh(c*x)/(e*x+d),x)","\int \frac{\operatorname{asinh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral(asinh(c*x)/(d + e*x), x)","F",0
2,0,0,0,0.000000," ","integrate(asinh(c*x)**2/(e*x+d),x)","\int \frac{\operatorname{asinh}^{2}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral(asinh(c*x)**2/(d + e*x), x)","F",0
3,0,0,0,0.000000," ","integrate(asinh(c*x)**3/(e*x+d),x)","\int \frac{\operatorname{asinh}^{3}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral(asinh(c*x)**3/(d + e*x), x)","F",0
4,1,316,0,1.479095," ","integrate((e*x+d)**3*(a+b*asinh(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{asinh}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{asinh}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{asinh}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{asinh}{\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{asinh}{\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{asinh}{\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*asinh(c*x) + 3*b*d**2*e*x**2*asinh(c*x)/2 + b*d*e**2*x**3*asinh(c*x) + b*e**3*x**4*asinh(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*asinh(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*asinh(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
5,1,190,0,0.660939," ","integrate((e*x+d)**2*(a+b*asinh(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{asinh}{\left(c x \right)} + b d e x^{2} \operatorname{asinh}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{asinh}{\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{asinh}{\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*asinh(c*x) + b*d*e*x**2*asinh(c*x) + b*e**2*x**3*asinh(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*asinh(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
6,1,99,0,0.302664," ","integrate((e*x+d)*(a+b*asinh(c*x)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + b d x \operatorname{asinh}{\left(c x \right)} + \frac{b e x^{2} \operatorname{asinh}{\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{asinh}{\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*asinh(c*x) + b*e*x**2*asinh(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*asinh(c*x)/(4*c**2), Ne(c, 0)), (a*(d*x + e*x**2/2), True))","A",0
7,1,26,0,0.133331," ","integrate(a+b*asinh(c*x),x)","a x + b \left(\begin{cases} x \operatorname{asinh}{\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*asinh(c*x) - sqrt(c**2*x**2 + 1)/c, Ne(c, 0)), (0, True))","A",0
8,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x), x)","F",0
9,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x+d)**2,x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x)**2, x)","F",0
10,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x+d)**3,x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x)**3, x)","F",0
11,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x+d)**4,x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x)**4, x)","F",0
12,1,743,0,3.944728," ","integrate((e*x+d)**3*(a+b*asinh(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{asinh}{\left(c x \right)} + 3 a b d^{2} e x^{2} \operatorname{asinh}{\left(c x \right)} + 2 a b d e^{2} x^{3} \operatorname{asinh}{\left(c x \right)} + \frac{a b e^{3} x^{4} \operatorname{asinh}{\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{asinh}{\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{asinh}{\left(c x \right)}}{16 c^{4}} + b^{2} d^{3} x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} d^{3} x + \frac{3 b^{2} d^{2} e x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{3 b^{2} d^{2} e x^{2}}{4} + b^{2} d e^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)} + \frac{2 b^{2} d e^{2} x^{3}}{9} + \frac{b^{2} e^{3} x^{4} \operatorname{asinh}^{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{asinh}{\left(c x \right)}}{c} - \frac{3 b^{2} d^{2} e x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2 c} - \frac{2 b^{2} d e^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c} - \frac{b^{2} e^{3} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{8 c} + \frac{3 b^{2} d^{2} e \operatorname{asinh}^{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{asinh}{\left(c x \right)}}{3 c^{3}} + \frac{3 b^{2} e^{3} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{16 c^{3}} - \frac{3 b^{2} e^{3} \operatorname{asinh}^{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*asinh(c*x) + 3*a*b*d**2*e*x**2*asinh(c*x) + 2*a*b*d*e**2*x**3*asinh(c*x) + a*b*e**3*x**4*asinh(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*asinh(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*asinh(c*x)/(16*c**4) + b**2*d**3*x*asinh(c*x)**2 + 2*b**2*d**3*x + 3*b**2*d**2*e*x**2*asinh(c*x)**2/2 + 3*b**2*d**2*e*x**2/4 + b**2*d*e**2*x**3*asinh(c*x)**2 + 2*b**2*d*e**2*x**3/9 + b**2*e**3*x**4*asinh(c*x)**2/4 + b**2*e**3*x**4/32 - 2*b**2*d**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - 3*b**2*d**2*e*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(2*c) - 2*b**2*d*e**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c) - b**2*e**3*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(8*c) + 3*b**2*d**2*e*asinh(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)*asinh(c*x)/(3*c**3) + 3*b**2*e**3*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(16*c**3) - 3*b**2*e**3*asinh(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
13,1,454,0,1.721119," ","integrate((e*x+d)**2*(a+b*asinh(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{asinh}{\left(c x \right)} + 2 a b d e x^{2} \operatorname{asinh}{\left(c x \right)} + \frac{2 a b e^{2} x^{3} \operatorname{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c x \right)} + 2 b^{2} d^{2} x + b^{2} d e x^{2} \operatorname{asinh}^{2}{\left(c x \right)} + \frac{b^{2} d e x^{2}}{2} + \frac{b^{2} e^{2} x^{3} \operatorname{asinh}^{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{asinh}{\left(c x \right)}}{c} - \frac{b^{2} d e x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{c} - \frac{2 b^{2} e^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c} + \frac{b^{2} d e \operatorname{asinh}^{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{asinh}{\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*asinh(c*x) + 2*a*b*d*e*x**2*asinh(c*x) + 2*a*b*e**2*x**3*asinh(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*asinh(c*x)/c**2 + 4*a*b*e**2*sqrt(c**2*x**2 + 1)/(9*c**3) + b**2*d**2*x*asinh(c*x)**2 + 2*b**2*d**2*x + b**2*d*e*x**2*asinh(c*x)**2 + b**2*d*e*x**2/2 + b**2*e**2*x**3*asinh(c*x)**2/3 + 2*b**2*e**2*x**3/27 - 2*b**2*d**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - b**2*d*e*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - 2*b**2*e**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c) + b**2*d*e*asinh(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)*asinh(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
14,1,233,0,0.854688," ","integrate((e*x+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} a^{2} d x + \frac{a^{2} e x^{2}}{2} + 2 a b d x \operatorname{asinh}{\left(c x \right)} + a b e x^{2} \operatorname{asinh}{\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{asinh}{\left(c x \right)}}{2 c^{2}} + b^{2} d x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} d x + \frac{b^{2} e x^{2} \operatorname{asinh}^{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{asinh}{\left(c x \right)}}{c} - \frac{b^{2} e x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2 c} + \frac{b^{2} e \operatorname{asinh}^{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*asinh(c*x) + a*b*e*x**2*asinh(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*asinh(c*x)/(2*c**2) + b**2*d*x*asinh(c*x)**2 + 2*b**2*d*x + b**2*e*x**2*asinh(c*x)**2/2 + b**2*e*x**2/4 - 2*b**2*d*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - b**2*e*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(2*c) + b**2*e*asinh(c*x)**2/(4*c**2), Ne(c, 0)), (a**2*(d*x + e*x**2/2), True))","A",0
15,1,82,0,0.278458," ","integrate((a+b*asinh(c*x))**2,x)","\begin{cases} a^{2} x + 2 a b x \operatorname{asinh}{\left(c x \right)} - \frac{2 a b \sqrt{c^{2} x^{2} + 1}}{c} + b^{2} x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} x - \frac{2 b^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\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*asinh(c*x) - 2*a*b*sqrt(c**2*x**2 + 1)/c + b**2*x*asinh(c*x)**2 + 2*b**2*x - 2*b**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/c, Ne(c, 0)), (a**2*x, True))","A",0
16,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d + e*x), x)","F",0
17,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d + e*x)**2, x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d + e*x)**3, x)","F",0
19,0,0,0,0.000000," ","integrate((e*x+d)**3/(a+b*asinh(c*x)),x)","\int \frac{\left(d + e x\right)^{3}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*asinh(c*x)), x)","F",0
20,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*asinh(c*x)),x)","\int \frac{\left(d + e x\right)^{2}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*asinh(c*x)), x)","F",0
21,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*asinh(c*x)),x)","\int \frac{d + e x}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)/(a + b*asinh(c*x)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x)),x)","\int \frac{1}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(1/(a + b*asinh(c*x)), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(d + e*x)), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(d + e*x)**2), x)","F",0
25,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*asinh(c*x))**2,x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*asinh(c*x))**2, x)","F",0
26,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*asinh(c*x))**2,x)","\int \frac{d + e x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)/(a + b*asinh(c*x))**2, x)","F",0
27,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**(-2), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(d + e*x)), x)","F",0
29,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*asinh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(d + e*x)**2), x)","F",0
30,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*asinh(c*x))**2,x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2*(d + e*x)**m, x)","F",0
31,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*asinh(c*x)),x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*asinh(c*x))*(d + e*x)**m, x)","F",0
32,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*asinh(c*x)),x)","\int \frac{\left(d + e x\right)^{m}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*asinh(c*x)), x)","F",0
33,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*asinh(c*x))**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*asinh(c*x))**2, x)","F",0
34,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))*(f + g*x)**3, x)","F",0
35,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))*(f + g*x)**2, x)","F",0
36,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))*(f + g*x), x)","F",0
37,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/(g*x+f),x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/(f + g*x), x)","F",0
38,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/(g*x+f)**2,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/(f + g*x)**2, x)","F",0
39,0,0,0,0.000000," ","integrate((g*x+f)**3*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))*(f + g*x)**3, x)","F",0
40,0,0,0,0.000000," ","integrate((g*x+f)**2*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))*(f + g*x)**2, x)","F",0
41,0,0,0,0.000000," ","integrate((g*x+f)*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))*(f + g*x), x)","F",0
42,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))/(g*x+f),x)","\int \frac{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))/(f + g*x), x)","F",0
43,-1,0,0,0.000000," ","integrate((g*x+f)**3*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,-1,0,0,0.000000," ","integrate((g*x+f)**2*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate((g*x+f)*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))/(g*x+f),x)","\int \frac{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))/(f + g*x), x)","F",0
47,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{3}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))*(f + g*x)**3/sqrt(d*(c**2*x**2 + 1)), x)","F",0
48,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))*(f + g*x)**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
49,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(f + g x\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))*(f + g*x)/sqrt(d*(c**2*x**2 + 1)), x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(g*x+f)/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(sqrt(d*(c**2*x**2 + 1))*(f + g*x)), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(g*x+f)**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(sqrt(d*(c**2*x**2 + 1))*(f + g*x)**2), x)","F",0
53,-1,0,0,0.000000," ","integrate((a+b*asinh(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
54,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*ln(h*(g*x+f)**m)/(c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2*log(h*(f + g*x)**m)/sqrt(c**2*x**2 + 1), x)","F",0
55,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*ln(h*(g*x+f)**m)/(c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral((a + b*asinh(c*x))*log(h*(f + g*x)**m)/sqrt(c**2*x**2 + 1), x)","F",0
56,0,0,0,0.000000," ","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{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/sqrt(c**2*x**2 + 1), x)","F",0
57,0,0,0,0.000000," ","integrate(ln(h*(g*x+f)**m)/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{\log{\left(h \left(f + g x\right)^{m} \right)}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
58,1,255,0,1.437987," ","integrate(x**3*asinh(b*x+a),x)","\begin{cases} - \frac{a^{4} \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(a + b x \right)}}{32 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{asinh}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*asinh(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*asinh(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*asinh(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*asinh(a + b*x)/(32*b**4), Ne(b, 0)), (x**4*asinh(a)/4, True))","A",0
59,1,170,0,0.666285," ","integrate(x**2*asinh(b*x+a),x)","\begin{cases} \frac{a^{3} \operatorname{asinh}{\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{asinh}{\left(a + b x \right)}}{2 b^{3}} + \frac{x^{3} \operatorname{asinh}{\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{asinh}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asinh(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*asinh(a + b*x)/(2*b**3) + x**3*asinh(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*asinh(a)/3, True))","A",0
60,1,104,0,0.301610," ","integrate(x*asinh(b*x+a),x)","\begin{cases} - \frac{a^{2} \operatorname{asinh}{\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{asinh}{\left(a + b x \right)}}{2} - \frac{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{4 b} + \frac{\operatorname{asinh}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asinh}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asinh(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*asinh(a + b*x)/2 - x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(4*b) + asinh(a + b*x)/(4*b**2), Ne(b, 0)), (x**2*asinh(a)/2, True))","A",0
61,1,46,0,0.163962," ","integrate(asinh(b*x+a),x)","\begin{cases} \frac{a \operatorname{asinh}{\left(a + b x \right)}}{b} + x \operatorname{asinh}{\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{asinh}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asinh(a + b*x)/b + x*asinh(a + b*x) - sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/b, Ne(b, 0)), (x*asinh(a), True))","A",0
62,0,0,0,0.000000," ","integrate(asinh(b*x+a)/x,x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asinh(a + b*x)/x, x)","F",0
63,0,0,0,0.000000," ","integrate(asinh(b*x+a)/x**2,x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(a + b*x)/x**2, x)","F",0
64,0,0,0,0.000000," ","integrate(asinh(b*x+a)/x**3,x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a + b*x)/x**3, x)","F",0
65,0,0,0,0.000000," ","integrate(asinh(b*x+a)/x**4,x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{x^{4}}\, dx"," ",0,"Integral(asinh(a + b*x)/x**4, x)","F",0
66,0,0,0,0.000000," ","integrate(asinh(b*x+a)/x**5,x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{x^{5}}\, dx"," ",0,"Integral(asinh(a + b*x)/x**5, x)","F",0
67,1,366,0,3.106998," ","integrate(x**3*asinh(b*x+a)**2,x)","\begin{cases} - \frac{a^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(a + b x \right)}}{24 b^{3}} + \frac{3 a^{2} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(a + b x \right)}}{48 b^{4}} + \frac{x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(a + b x \right)}}{16 b^{3}} - \frac{3 \operatorname{asinh}^{2}{\left(a + b x \right)}}{32 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{asinh}^{2}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*asinh(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)*asinh(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)*asinh(a + b*x)/(24*b**3) + 3*a**2*asinh(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)*asinh(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)*asinh(a + b*x)/(48*b**4) + x**4*asinh(a + b*x)**2/4 + x**4/32 - x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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)*asinh(a + b*x)/(16*b**3) - 3*asinh(a + b*x)**2/(32*b**4), Ne(b, 0)), (x**4*asinh(a)**2/4, True))","A",0
68,1,243,0,1.384727," ","integrate(x**2*asinh(b*x+a)**2,x)","\begin{cases} \frac{a^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(a + b x \right)}}{9 b^{2}} - \frac{a \operatorname{asinh}^{2}{\left(a + b x \right)}}{2 b^{3}} + \frac{x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(a + b x \right)}}{9 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{asinh}^{2}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asinh(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)*asinh(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)*asinh(a + b*x)/(9*b**2) - a*asinh(a + b*x)**2/(2*b**3) + x**3*asinh(a + b*x)**2/3 + 2*x**3/27 - 2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/(9*b) - 4*x/(9*b**2) + 4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/(9*b**3), Ne(b, 0)), (x**3*asinh(a)**2/3, True))","A",0
69,1,138,0,0.676045," ","integrate(x*asinh(b*x+a)**2,x)","\begin{cases} - \frac{a^{2} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{2 b^{2}} + \frac{x^{2} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{2 b} + \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asinh}^{2}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asinh(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)*asinh(a + b*x)/(2*b**2) + x**2*asinh(a + b*x)**2/2 + x**2/4 - x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/(2*b) + asinh(a + b*x)**2/(4*b**2), Ne(b, 0)), (x**2*asinh(a)**2/2, True))","A",0
70,1,63,0,0.261920," ","integrate(asinh(b*x+a)**2,x)","\begin{cases} \frac{a \operatorname{asinh}^{2}{\left(a + b x \right)}}{b} + x \operatorname{asinh}^{2}{\left(a + b x \right)} + 2 x - \frac{2 \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \operatorname{asinh}^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asinh(a + b*x)**2/b + x*asinh(a + b*x)**2 + 2*x - 2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/b, Ne(b, 0)), (x*asinh(a)**2, True))","A",0
71,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2/x,x)","\int \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asinh(a + b*x)**2/x, x)","F",0
72,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2/x**2,x)","\int \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(a + b*x)**2/x**2, x)","F",0
73,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2/x**3,x)","\int \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a + b*x)**2/x**3, x)","F",0
74,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2/x**4,x)","\int \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{x^{4}}\, dx"," ",0,"Integral(asinh(a + b*x)**2/x**4, x)","F",0
75,1,432,0,3.036321," ","integrate(x**2*asinh(b*x+a)**3,x)","\begin{cases} \frac{a^{3} \operatorname{asinh}^{3}{\left(a + b x \right)}}{3 b^{3}} + \frac{85 a^{3} \operatorname{asinh}{\left(a + b x \right)}}{18 b^{3}} + \frac{11 a^{2} x \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(a + b x \right)}}{6 b} + \frac{5 a x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{2 b^{3}} - \frac{25 a \operatorname{asinh}{\left(a + b x \right)}}{12 b^{3}} + \frac{x^{3} \operatorname{asinh}^{3}{\left(a + b x \right)}}{3} + \frac{2 x^{3} \operatorname{asinh}{\left(a + b x \right)}}{9} - \frac{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asinh(a + b*x)**3/(3*b**3) + 85*a**3*asinh(a + b*x)/(18*b**3) + 11*a**2*x*asinh(a + b*x)/(3*b**2) - 11*a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/(6*b) + 5*a*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)**3/(2*b**3) - 25*a*asinh(a + b*x)/(12*b**3) + x**3*asinh(a + b*x)**3/3 + 2*x**3*asinh(a + b*x)/9 - x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/(3*b**2) + 2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a)**3/3, True))","A",0
76,1,248,0,1.294836," ","integrate(x*asinh(b*x+a)**3,x)","\begin{cases} - \frac{a^{2} \operatorname{asinh}^{3}{\left(a + b x \right)}}{2 b^{2}} - \frac{21 a^{2} \operatorname{asinh}{\left(a + b x \right)}}{4 b^{2}} - \frac{9 a x \operatorname{asinh}{\left(a + b x \right)}}{2 b} + \frac{9 a \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{2} + \frac{3 x^{2} \operatorname{asinh}{\left(a + b x \right)}}{4} - \frac{3 x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{4 b^{2}} + \frac{3 \operatorname{asinh}{\left(a + b x \right)}}{8 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asinh}^{3}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asinh(a + b*x)**3/(2*b**2) - 21*a**2*asinh(a + b*x)/(4*b**2) - 9*a*x*asinh(a + b*x)/(2*b) + 9*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)**3/2 + 3*x**2*asinh(a + b*x)/4 - 3*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**2/(4*b) - 3*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(8*b) + asinh(a + b*x)**3/(4*b**2) + 3*asinh(a + b*x)/(8*b**2), Ne(b, 0)), (x**2*asinh(a)**3/2, True))","A",0
77,1,109,0,0.598415," ","integrate(asinh(b*x+a)**3,x)","\begin{cases} \frac{a \operatorname{asinh}^{3}{\left(a + b x \right)}}{b} + \frac{6 a \operatorname{asinh}{\left(a + b x \right)}}{b} + x \operatorname{asinh}^{3}{\left(a + b x \right)} + 6 x \operatorname{asinh}{\left(a + b x \right)} - \frac{3 \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asinh(a + b*x)**3/b + 6*a*asinh(a + b*x)/b + x*asinh(a + b*x)**3 + 6*x*asinh(a + b*x) - 3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**2/b - 6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/b, Ne(b, 0)), (x*asinh(a)**3, True))","A",0
78,0,0,0,0.000000," ","integrate(asinh(b*x+a)**3/x,x)","\int \frac{\operatorname{asinh}^{3}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asinh(a + b*x)**3/x, x)","F",0
79,0,0,0,0.000000," ","integrate(asinh(b*x+a)**3/x**2,x)","\int \frac{\operatorname{asinh}^{3}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(a + b*x)**3/x**2, x)","F",0
80,0,0,0,0.000000," ","integrate(asinh(b*x+a)**3/x**3,x)","\int \frac{\operatorname{asinh}^{3}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a + b*x)**3/x**3, x)","F",0
81,0,0,0,0.000000," ","integrate(x**2/asinh(b*x+a),x)","\int \frac{x^{2}}{\operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asinh(a + b*x), x)","F",0
82,0,0,0,0.000000," ","integrate(x/asinh(b*x+a),x)","\int \frac{x}{\operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asinh(a + b*x), x)","F",0
83,0,0,0,0.000000," ","integrate(1/asinh(b*x+a),x)","\int \frac{1}{\operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/asinh(a + b*x), x)","F",0
84,0,0,0,0.000000," ","integrate(1/x/asinh(b*x+a),x)","\int \frac{1}{x \operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asinh(a + b*x)), x)","F",0
85,0,0,0,0.000000," ","integrate(x**2/asinh(b*x+a)**2,x)","\int \frac{x^{2}}{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asinh(a + b*x)**2, x)","F",0
86,0,0,0,0.000000," ","integrate(x/asinh(b*x+a)**2,x)","\int \frac{x}{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asinh(a + b*x)**2, x)","F",0
87,0,0,0,0.000000," ","integrate(1/asinh(b*x+a)**2,x)","\int \frac{1}{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(asinh(a + b*x)**(-2), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x/asinh(b*x+a)**2,x)","\int \frac{1}{x \operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asinh(a + b*x)**2), x)","F",0
89,0,0,0,0.000000," ","integrate(x**2/asinh(b*x+a)**3,x)","\int \frac{x^{2}}{\operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asinh(a + b*x)**3, x)","F",0
90,0,0,0,0.000000," ","integrate(x/asinh(b*x+a)**3,x)","\int \frac{x}{\operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asinh(a + b*x)**3, x)","F",0
91,0,0,0,0.000000," ","integrate(1/asinh(b*x+a)**3,x)","\int \frac{1}{\operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(asinh(a + b*x)**(-3), x)","F",0
92,0,0,0,0.000000," ","integrate(1/x/asinh(b*x+a)**3,x)","\int \frac{1}{x \operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asinh(a + b*x)**3), x)","F",0
93,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(d*x+c))**n,x)","\int x^{m} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x**m*(a + b*asinh(c + d*x))**n, x)","F",0
94,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(d*x+c))**n,x)","\int x^{2} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c + d*x))**n, x)","F",0
95,0,0,0,0.000000," ","integrate(x*(a+b*asinh(d*x+c))**n,x)","\int x \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x*(a + b*asinh(c + d*x))**n, x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**n,x)","\int \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**n, x)","F",0
97,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**n/x,x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{n}}{x}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**n/x, x)","F",0
98,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(d*x+c))**(1/2),x)","\int x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*asinh(c + d*x)), x)","F",0
99,0,0,0,0.000000," ","integrate(x*(a+b*asinh(d*x+c))**(1/2),x)","\int x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x*sqrt(a + b*asinh(c + d*x)), x)","F",0
100,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(1/2),x)","\int \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c + d*x)), x)","F",0
101,0,0,0,0.000000," ","integrate(x*(a+b*asinh(d*x+c))**(3/2),x)","\int x \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*asinh(c + d*x))**(3/2), x)","F",0
102,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(3/2),x)","\int \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(x*(a+b*asinh(d*x+c))**(5/2),x)","\int x \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(a + b*asinh(c + d*x))**(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(5/2),x)","\int \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate(x**2/(a+b*asinh(d*x+c))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*asinh(c + d*x)), x)","F",0
106,0,0,0,0.000000," ","integrate(x/(a+b*asinh(d*x+c))**(1/2),x)","\int \frac{x}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(x/sqrt(a + b*asinh(c + d*x)), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asinh(c + d*x)), x)","F",0
108,0,0,0,0.000000," ","integrate(x/(a+b*asinh(d*x+c))**(3/2),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a + b*asinh(c + d*x))**(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-3/2), x)","F",0
110,0,0,0,0.000000," ","integrate(x/(a+b*asinh(d*x+c))**(5/2),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/(a + b*asinh(c + d*x))**(5/2), x)","F",0
111,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-5/2), x)","F",0
112,0,0,0,0.000000," ","integrate(x/(a+b*asinh(d*x+c))**(7/2),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x/(a + b*asinh(c + d*x))**(7/2), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-7/2), x)","F",0
114,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asinh(d*x+c)),x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asinh(c + d*x)), x)","F",0
115,1,527,0,3.503894," ","integrate((d*e*x+c*e)**4*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{5 d} + b c^{4} e^{4} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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*asinh(c + d*x)/(5*d) + b*c**4*e**4*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c)), True))","A",0
116,1,394,0,1.692326," ","integrate((d*e*x+c*e)**3*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{4 d} + b c^{3} e^{3} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(4*d) + b*c**3*e**3*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asinh(c)), True))","A",0
117,1,258,0,0.769327," ","integrate((d*e*x+c*e)**2*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{3 d} + b c^{2} e^{2} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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*asinh(c + d*x)/(3*d) + b*c**2*e**2*x*asinh(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*asinh(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*asinh(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*asinh(c)), True))","A",0
118,1,148,0,0.334540," ","integrate((d*e*x+c*e)*(a+b*asinh(d*x+c)),x)","\begin{cases} a c e x + \frac{a d e x^{2}}{2} + \frac{b c^{2} e \operatorname{asinh}{\left(c + d x \right)}}{2 d} + b c e x \operatorname{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asinh}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*e*x + a*d*e*x**2/2 + b*c**2*e*asinh(c + d*x)/(2*d) + b*c*e*x*asinh(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*asinh(c + d*x)/2 - b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)/4 + b*e*asinh(c + d*x)/(4*d), Ne(d, 0)), (c*e*x*(a + b*asinh(c)), True))","A",0
119,1,51,0,0.157516," ","integrate(a+b*asinh(d*x+c),x)","a x + b \left(\begin{cases} \frac{c \operatorname{asinh}{\left(c + d x \right)}}{d} + x \operatorname{asinh}{\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{asinh}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((c*asinh(c + d*x)/d + x*asinh(c + d*x) - sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)/d, Ne(d, 0)), (x*asinh(c), True))","A",0
120,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))/(d*e*x+c*e),x)","\frac{\int \frac{a}{c + d x}\, dx + \int \frac{b \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a/(c + d*x), x) + Integral(b*asinh(c + d*x)/(c + d*x), x))/e","F",0
121,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}{\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*asinh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
122,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}{\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*asinh(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
123,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}{\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*asinh(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
124,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}{\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*asinh(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
125,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}{\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*asinh(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
126,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asinh(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asinh(c + d*x))**2, x)","F",0
127,1,1268,0,7.461868," ","integrate((d*e*x+c*e)**4*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{5 d} + 2 a b c^{4} e^{4} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{5 d} + b^{2} c^{4} e^{4} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{25 d} + 2 b^{2} c^{3} d e^{4} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{25} + 2 b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{75 d} + b^{2} c d^{3} e^{4} x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{75} + \frac{b^{2} d^{4} e^{4} x^{5} \operatorname{asinh}^{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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{75 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(5*d) + 2*a*b*c**4*e**4*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)**2/(5*d) + b**2*c**4*e**4*x*asinh(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)*asinh(c + d*x)/(25*d) + 2*b**2*c**3*d*e**4*x**2*asinh(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)*asinh(c + d*x)/25 + 2*b**2*c**2*d**2*e**4*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(75*d) + b**2*c*d**3*e**4*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/75 + b**2*d**4*e**4*x**5*asinh(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)*asinh(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)*asinh(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)*asinh(c + d*x)/(75*d), Ne(d, 0)), (c**4*e**4*x*(a + b*asinh(c))**2, True))","A",0
128,1,916,0,4.593104," ","integrate((d*e*x+c*e)**3*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{2 d} + 2 a b c^{3} e^{3} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{16 d} + \frac{b^{2} c^{4} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{4 d} + b^{2} c^{3} e^{3} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{8 d} + \frac{3 b^{2} c^{2} d e^{3} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{8} + b^{2} c d^{2} e^{3} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{16 d} + \frac{b^{2} d^{3} e^{3} x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{16} - \frac{3 b^{2} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(2*d) + 2*a*b*c**3*e**3*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)/(16*d) + b**2*c**4*e**3*asinh(c + d*x)**2/(4*d) + b**2*c**3*e**3*x*asinh(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)*asinh(c + d*x)/(8*d) + 3*b**2*c**2*d*e**3*x**2*asinh(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)*asinh(c + d*x)/8 + b**2*c*d**2*e**3*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(16*d) + b**2*d**3*e**3*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/16 - 3*b**2*e**3*asinh(c + d*x)**2/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asinh(c))**2, True))","A",0
129,1,610,0,1.863792," ","integrate((d*e*x+c*e)**2*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{3 d} + 2 a b c^{2} e^{2} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{3 d} + b^{2} c^{2} e^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{9 d} + b^{2} c d e^{2} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{9} + \frac{b^{2} d^{2} e^{2} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(3*d) + 2*a*b*c**2*e**2*x*asinh(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*asinh(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*asinh(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*asinh(c + d*x)**2/(3*d) + b**2*c**2*e**2*x*asinh(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)*asinh(c + d*x)/(9*d) + b**2*c*d*e**2*x**2*asinh(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)*asinh(c + d*x)/9 + b**2*d**2*e**2*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(9*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asinh(c))**2, True))","A",0
130,1,335,0,0.857292," ","integrate((d*e*x+c*e)*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{d} + 2 a b c e x \operatorname{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{2 d} + \frac{b^{2} c^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{2 d} + b^{2} c e x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{2 d} + \frac{b^{2} d e x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{2} + \frac{b^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/d + 2*a*b*c*e*x*asinh(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*asinh(c + d*x) - a*b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)/2 + a*b*e*asinh(c + d*x)/(2*d) + b**2*c**2*e*asinh(c + d*x)**2/(2*d) + b**2*c*e*x*asinh(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)*asinh(c + d*x)/(2*d) + b**2*d*e*x**2*asinh(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)*asinh(c + d*x)/2 + b**2*e*asinh(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*asinh(c))**2, True))","A",0
131,1,143,0,0.324908," ","integrate((a+b*asinh(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{2 a b c \operatorname{asinh}{\left(c + d x \right)}}{d} + 2 a b x \operatorname{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{d} + b^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asinh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*c*asinh(c + d*x)/d + 2*a*b*x*asinh(c + d*x) - 2*a*b*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)/d + b**2*c*asinh(c + d*x)**2/d + b**2*x*asinh(c + d*x)**2 + 2*b**2*x - 2*b**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/d, Ne(d, 0)), (x*(a + b*asinh(c))**2, True))","A",0
132,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2/(d*e*x+c*e),x)","\frac{\int \frac{a^{2}}{c + d x}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2/(c + d*x), x) + Integral(b**2*asinh(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*asinh(c + d*x)/(c + d*x), x))/e","F",0
133,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{2 a b \operatorname{asinh}{\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*asinh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(2*a*b*asinh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
134,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}{\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*asinh(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*asinh(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
135,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}{\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*asinh(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*asinh(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
136,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asinh(d*x+c))**3,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asinh(c + d*x))**3, x)","F",0
137,1,2518,0,17.075170," ","integrate((d*e*x+c*e)**4*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{5 d} + 3 a^{2} b c^{4} e^{4} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{5 d} + 3 a b^{2} c^{4} e^{4} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{25 d} + 6 a b^{2} c^{3} d e^{4} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{25} + 6 a b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{25 d} + 3 a b^{2} c d^{3} e^{4} x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{25} + \frac{3 a b^{2} d^{4} e^{4} x^{5} \operatorname{asinh}^{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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{25 d} + \frac{b^{3} c^{5} e^{4} \operatorname{asinh}^{3}{\left(c + d x \right)}}{5 d} + \frac{6 b^{3} c^{5} e^{4} \operatorname{asinh}{\left(c + d x \right)}}{125 d} + b^{3} c^{4} e^{4} x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{6 b^{3} c^{4} e^{4} x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{12 b^{3} c^{3} d e^{4} x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{75 d} + 2 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{12 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{6 b^{3} c d^{3} e^{4} x^{4} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{25 d} + \frac{b^{3} d^{4} e^{4} x^{5} \operatorname{asinh}^{3}{\left(c + d x \right)}}{5} + \frac{6 b^{3} d^{4} e^{4} x^{5} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}{\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*asinh(c + d*x)/(5*d) + 3*a**2*b*c**4*e**4*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)**2/(5*d) + 3*a*b**2*c**4*e**4*x*asinh(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)*asinh(c + d*x)/(25*d) + 6*a*b**2*c**3*d*e**4*x**2*asinh(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)*asinh(c + d*x)/25 + 6*a*b**2*c**2*d**2*e**4*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(25*d) + 3*a*b**2*c*d**3*e**4*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/25 + 3*a*b**2*d**4*e**4*x**5*asinh(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)*asinh(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)*asinh(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)*asinh(c + d*x)/(25*d) + b**3*c**5*e**4*asinh(c + d*x)**3/(5*d) + 6*b**3*c**5*e**4*asinh(c + d*x)/(125*d) + b**3*c**4*e**4*x*asinh(c + d*x)**3 + 6*b**3*c**4*e**4*x*asinh(c + d*x)/25 - 3*b**3*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 12*b**3*c**3*d*e**4*x**2*asinh(c + d*x)/25 - 12*b**3*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/(75*d) + 2*b**3*c**2*d**2*e**4*x**3*asinh(c + d*x)**3 + 12*b**3*c**2*d**2*e**4*x**3*asinh(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)*asinh(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*asinh(c + d*x)/25 + 4*b**3*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 6*b**3*c*d**3*e**4*x**4*asinh(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)*asinh(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*asinh(c + d*x)/25 + 8*b**3*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/(25*d) + b**3*d**4*e**4*x**5*asinh(c + d*x)**3/5 + 6*b**3*d**4*e**4*x**5*asinh(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)*asinh(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*asinh(c + d*x)/75 + 4*b**3*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/25 - 8*b**3*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c))**3, True))","A",0
138,1,1828,0,10.071874," ","integrate((d*e*x+c*e)**3*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{4 d} + 3 a^{2} b c^{3} e^{3} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{32 d} + \frac{3 a b^{2} c^{4} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{4 d} + 3 a b^{2} c^{3} e^{3} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{8 d} + \frac{9 a b^{2} c^{2} d e^{3} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{8} + 3 a b^{2} c d^{2} e^{3} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{16 d} + \frac{3 a b^{2} d^{3} e^{3} x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{16} - \frac{9 a b^{2} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{32 d} + \frac{b^{3} c^{4} e^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{4 d} + \frac{3 b^{3} c^{4} e^{3} \operatorname{asinh}{\left(c + d x \right)}}{32 d} + b^{3} c^{3} e^{3} x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c^{3} e^{3} x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{2} + \frac{9 b^{3} c^{2} d e^{3} x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{32 d} + b^{3} c d^{2} e^{3} x^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c d^{2} e^{3} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{4} + \frac{3 b^{3} d^{3} e^{3} x^{4} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{32 d} - \frac{45 b^{3} e^{3} \operatorname{asinh}{\left(c + d x \right)}}{256 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(4*d) + 3*a**2*b*c**3*e**3*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)/(32*d) + 3*a*b**2*c**4*e**3*asinh(c + d*x)**2/(4*d) + 3*a*b**2*c**3*e**3*x*asinh(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)*asinh(c + d*x)/(8*d) + 9*a*b**2*c**2*d*e**3*x**2*asinh(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)*asinh(c + d*x)/8 + 3*a*b**2*c*d**2*e**3*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(16*d) + 3*a*b**2*d**3*e**3*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/16 - 9*a*b**2*e**3*asinh(c + d*x)**2/(32*d) + b**3*c**4*e**3*asinh(c + d*x)**3/(4*d) + 3*b**3*c**4*e**3*asinh(c + d*x)/(32*d) + b**3*c**3*e**3*x*asinh(c + d*x)**3 + 3*b**3*c**3*e**3*x*asinh(c + d*x)/8 - 3*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/2 + 9*b**3*c**2*d*e**3*x**2*asinh(c + d*x)/16 - 9*b**3*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/(32*d) + b**3*c*d**2*e**3*x**3*asinh(c + d*x)**3 + 3*b**3*c*d**2*e**3*x**3*asinh(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)*asinh(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*asinh(c + d*x)/16 + 9*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/4 + 3*b**3*d**3*e**3*x**4*asinh(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)*asinh(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*asinh(c + d*x)/32 + 9*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/(32*d) - 45*b**3*e**3*asinh(c + d*x)/(256*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asinh(c))**3, True))","A",0
139,1,1173,0,4.994031," ","integrate((d*e*x+c*e)**2*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{d} + 3 a^{2} b c^{2} e^{2} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} c^{2} e^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{3 d} + 3 a b^{2} c d e^{2} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{3} + a b^{2} d^{2} e^{2} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{3 d} + \frac{b^{3} c^{3} e^{2} \operatorname{asinh}^{3}{\left(c + d x \right)}}{3 d} + \frac{2 b^{3} c^{3} e^{2} \operatorname{asinh}{\left(c + d x \right)}}{9 d} + b^{3} c^{2} e^{2} x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{2 b^{3} c^{2} e^{2} x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{2 b^{3} c d e^{2} x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{3 d} + \frac{b^{3} d^{2} e^{2} x^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{3} + \frac{2 b^{3} d^{2} e^{2} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}{\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*asinh(c + d*x)/d + 3*a**2*b*c**2*e**2*x*asinh(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*asinh(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*asinh(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*asinh(c + d*x)**2/d + 3*a*b**2*c**2*e**2*x*asinh(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)*asinh(c + d*x)/(3*d) + 3*a*b**2*c*d*e**2*x**2*asinh(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)*asinh(c + d*x)/3 + a*b**2*d**2*e**2*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(3*d) + b**3*c**3*e**2*asinh(c + d*x)**3/(3*d) + 2*b**3*c**3*e**2*asinh(c + d*x)/(9*d) + b**3*c**2*e**2*x*asinh(c + d*x)**3 + 2*b**3*c**2*e**2*x*asinh(c + d*x)/3 - b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 2*b**3*c*d*e**2*x**2*asinh(c + d*x)/3 - 2*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/(3*d) + b**3*d**2*e**2*x**3*asinh(c + d*x)**3/3 + 2*b**3*d**2*e**2*x**3*asinh(c + d*x)/9 - b**3*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/3 + 2*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c))**3, True))","A",0
140,1,685,0,2.081740," ","integrate((d*e*x+c*e)*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{2 d} + 3 a^{2} b c e x \operatorname{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{4 d} + \frac{3 a b^{2} c^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{2 d} + 3 a b^{2} c e x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{2 d} + \frac{3 a b^{2} d e x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{2} + \frac{3 a b^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{4 d} + \frac{b^{3} c^{2} e \operatorname{asinh}^{3}{\left(c + d x \right)}}{2 d} + \frac{3 b^{3} c^{2} e \operatorname{asinh}{\left(c + d x \right)}}{4 d} + b^{3} c e x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c e x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{2} + \frac{3 b^{3} d e x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{4 d} + \frac{3 b^{3} e \operatorname{asinh}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(2*d) + 3*a**2*b*c*e*x*asinh(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*asinh(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*asinh(c + d*x)/(4*d) + 3*a*b**2*c**2*e*asinh(c + d*x)**2/(2*d) + 3*a*b**2*c*e*x*asinh(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)*asinh(c + d*x)/(2*d) + 3*a*b**2*d*e*x**2*asinh(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)*asinh(c + d*x)/2 + 3*a*b**2*e*asinh(c + d*x)**2/(4*d) + b**3*c**2*e*asinh(c + d*x)**3/(2*d) + 3*b**3*c**2*e*asinh(c + d*x)/(4*d) + b**3*c*e*x*asinh(c + d*x)**3 + 3*b**3*c*e*x*asinh(c + d*x)/2 - 3*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/2 + 3*b**3*d*e*x**2*asinh(c + d*x)/4 - 3*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/(4*d) + 3*b**3*e*asinh(c + d*x)/(8*d), Ne(d, 0)), (c*e*x*(a + b*asinh(c))**3, True))","A",0
141,1,282,0,0.804208," ","integrate((a+b*asinh(d*x+c))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b c \operatorname{asinh}{\left(c + d x \right)}}{d} + 3 a^{2} b x \operatorname{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{d} + \frac{b^{3} c \operatorname{asinh}^{3}{\left(c + d x \right)}}{d} + \frac{6 b^{3} c \operatorname{asinh}{\left(c + d x \right)}}{d} + b^{3} x \operatorname{asinh}^{3}{\left(c + d x \right)} + 6 b^{3} x \operatorname{asinh}{\left(c + d x \right)} - \frac{3 b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*c*asinh(c + d*x)/d + 3*a**2*b*x*asinh(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*asinh(c + d*x)**2/d + 3*a*b**2*x*asinh(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)*asinh(c + d*x)/d + b**3*c*asinh(c + d*x)**3/d + 6*b**3*c*asinh(c + d*x)/d + b**3*x*asinh(c + d*x)**3 + 6*b**3*x*asinh(c + d*x) - 3*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c))**3, True))","A",0
142,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3/(d*e*x+c*e),x)","\frac{\int \frac{a^{3}}{c + d x}\, dx + \int \frac{b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a^{2} b \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**3/(c + d*x), x) + Integral(b**3*asinh(c + d*x)**3/(c + d*x), x) + Integral(3*a*b**2*asinh(c + d*x)**2/(c + d*x), x) + Integral(3*a**2*b*asinh(c + d*x)/(c + d*x), x))/e","F",0
143,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{3}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a^{2} b \operatorname{asinh}{\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*asinh(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a*b**2*asinh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a**2*b*asinh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
144,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}^{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{asinh}{\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*asinh(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*asinh(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*asinh(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
145,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}^{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{asinh}{\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*asinh(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*asinh(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*asinh(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
146,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asinh(d*x+c))**4,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asinh(c + d*x))**4, x)","F",0
147,1,2876,0,20.596817," ","integrate((d*e*x+c*e)**3*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{d} + 4 a^{3} b c^{3} e^{3} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} c^{4} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{2 d} + 6 a^{2} b^{2} c^{3} e^{3} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{4 d} + 9 a^{2} b^{2} c^{2} d e^{3} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{4} + 6 a^{2} b^{2} c d^{2} e^{3} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} d^{3} e^{3} x^{4} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{8} - \frac{9 a^{2} b^{2} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{16 d} + \frac{a b^{3} c^{4} e^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} c^{4} e^{3} \operatorname{asinh}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c^{3} e^{3} x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} c^{3} e^{3} x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{9 a b^{3} c^{2} d e^{3} x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c d^{2} e^{3} x^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} c d^{2} e^{3} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} d^{3} e^{3} x^{4} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{8 d} - \frac{45 a b^{3} e^{3} \operatorname{asinh}{\left(c + d x \right)}}{64 d} + \frac{b^{4} c^{4} e^{3} \operatorname{asinh}^{4}{\left(c + d x \right)}}{4 d} + \frac{3 b^{4} c^{4} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c^{3} e^{3} x \operatorname{asinh}^{4}{\left(c + d x \right)} + \frac{3 b^{4} c^{3} e^{3} x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{32 d} + \frac{3 b^{4} c^{2} d e^{3} x^{2} \operatorname{asinh}^{4}{\left(c + d x \right)}}{2} + \frac{9 b^{4} c^{2} d e^{3} x^{2} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{32} - \frac{9 b^{4} c^{2} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c d^{2} e^{3} x^{3} \operatorname{asinh}^{4}{\left(c + d x \right)} + \frac{3 b^{4} c d^{2} e^{3} x^{3} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{32} - \frac{9 b^{4} c e^{3} x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{64 d} + \frac{b^{4} d^{3} e^{3} x^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}{4} + \frac{3 b^{4} d^{3} e^{3} x^{4} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{32} - \frac{9 b^{4} d e^{3} x^{2} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{64} - \frac{3 b^{4} e^{3} \operatorname{asinh}^{4}{\left(c + d x \right)}}{32 d} - \frac{45 b^{4} e^{3} \operatorname{asinh}^{2}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/d + 4*a**3*b*c**3*e**3*x*asinh(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*asinh(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*asinh(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*asinh(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*asinh(c + d*x)/(8*d) + 3*a**2*b**2*c**4*e**3*asinh(c + d*x)**2/(2*d) + 6*a**2*b**2*c**3*e**3*x*asinh(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)*asinh(c + d*x)/(4*d) + 9*a**2*b**2*c**2*d*e**3*x**2*asinh(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)*asinh(c + d*x)/4 + 6*a**2*b**2*c*d**2*e**3*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(8*d) + 3*a**2*b**2*d**3*e**3*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/8 - 9*a**2*b**2*e**3*asinh(c + d*x)**2/(16*d) + a*b**3*c**4*e**3*asinh(c + d*x)**3/d + 3*a*b**3*c**4*e**3*asinh(c + d*x)/(8*d) + 4*a*b**3*c**3*e**3*x*asinh(c + d*x)**3 + 3*a*b**3*c**3*e**3*x*asinh(c + d*x)/2 - 3*a*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 9*a*b**3*c**2*d*e**3*x**2*asinh(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)*asinh(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*asinh(c + d*x)/(8*d) + 4*a*b**3*c*d**2*e**3*x**3*asinh(c + d*x)**3 + 3*a*b**3*c*d**2*e**3*x**3*asinh(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)*asinh(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*asinh(c + d*x)/4 + 9*a*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 3*a*b**3*d**3*e**3*x**4*asinh(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)*asinh(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*asinh(c + d*x)/8 + 9*a*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/(8*d) - 45*a*b**3*e**3*asinh(c + d*x)/(64*d) + b**4*c**4*e**3*asinh(c + d*x)**4/(4*d) + 3*b**4*c**4*e**3*asinh(c + d*x)**2/(16*d) + b**4*c**3*e**3*x*asinh(c + d*x)**4 + 3*b**4*c**3*e**3*x*asinh(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)*asinh(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)*asinh(c + d*x)/(32*d) + 3*b**4*c**2*d*e**3*x**2*asinh(c + d*x)**4/2 + 9*b**4*c**2*d*e**3*x**2*asinh(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)*asinh(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)*asinh(c + d*x)/32 - 9*b**4*c**2*e**3*asinh(c + d*x)**2/(16*d) + b**4*c*d**2*e**3*x**3*asinh(c + d*x)**4 + 3*b**4*c*d**2*e**3*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/32 - 9*b**4*c*e**3*x*asinh(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)*asinh(c + d*x)**3/(8*d) + 45*b**4*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/(64*d) + b**4*d**3*e**3*x**4*asinh(c + d*x)**4/4 + 3*b**4*d**3*e**3*x**4*asinh(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)*asinh(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)*asinh(c + d*x)/32 - 9*b**4*d*e**3*x**2*asinh(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)*asinh(c + d*x)**3/8 + 45*b**4*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/64 - 3*b**4*e**3*asinh(c + d*x)**4/(32*d) - 45*b**4*e**3*asinh(c + d*x)**2/(128*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asinh(c))**4, True))","A",0
148,1,1889,0,9.645808," ","integrate((d*e*x+c*e)**2*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{3 d} + 4 a^{3} b c^{2} e^{2} x \operatorname{asinh}{\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{asinh}{\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{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c^{2} e^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{3 d} + 6 a^{2} b^{2} c d e^{2} x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{3} + 2 a^{2} b^{2} d^{2} e^{2} x^{3} \operatorname{asinh}^{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{asinh}{\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{asinh}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} c^{3} e^{2} \operatorname{asinh}^{3}{\left(c + d x \right)}}{3 d} + \frac{8 a b^{3} c^{3} e^{2} \operatorname{asinh}{\left(c + d x \right)}}{9 d} + 4 a b^{3} c^{2} e^{2} x \operatorname{asinh}^{3}{\left(c + d x \right)} + \frac{8 a b^{3} c^{2} e^{2} x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + \frac{8 a b^{3} c d e^{2} x^{2} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} d^{2} e^{2} x^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{3} + \frac{8 a b^{3} d^{2} e^{2} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\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{asinh}^{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{asinh}^{4}{\left(c + d x \right)}}{3 d} + \frac{4 b^{4} c^{3} e^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{9 d} + b^{4} c^{2} e^{2} x \operatorname{asinh}^{4}{\left(c + d x \right)} + \frac{4 b^{4} c^{2} e^{2} x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{27 d} + b^{4} c d e^{2} x^{2} \operatorname{asinh}^{4}{\left(c + d x \right)} + \frac{4 b^{4} c d e^{2} x^{2} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{27} - \frac{8 b^{4} c e^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{4} d^{2} e^{2} x^{3} \operatorname{asinh}^{4}{\left(c + d x \right)}}{3} + \frac{4 b^{4} d^{2} e^{2} x^{3} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{27} - \frac{8 b^{4} e^{2} x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{27 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/(3*d) + 4*a**3*b*c**2*e**2*x*asinh(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*asinh(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*asinh(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*asinh(c + d*x)**2/d + 6*a**2*b**2*c**2*e**2*x*asinh(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)*asinh(c + d*x)/(3*d) + 6*a**2*b**2*c*d*e**2*x**2*asinh(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)*asinh(c + d*x)/3 + 2*a**2*b**2*d**2*e**2*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/(3*d) + 4*a*b**3*c**3*e**2*asinh(c + d*x)**3/(3*d) + 8*a*b**3*c**3*e**2*asinh(c + d*x)/(9*d) + 4*a*b**3*c**2*e**2*x*asinh(c + d*x)**3 + 8*a*b**3*c**2*e**2*x*asinh(c + d*x)/3 - 4*a*b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 8*a*b**3*c*d*e**2*x**2*asinh(c + d*x)/3 - 8*a*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)/(3*d) + 4*a*b**3*d**2*e**2*x**3*asinh(c + d*x)**3/3 + 8*a*b**3*d**2*e**2*x**3*asinh(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)*asinh(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*asinh(c + d*x)/3 + 8*a*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**4/(3*d) + 4*b**4*c**3*e**2*asinh(c + d*x)**2/(9*d) + b**4*c**2*e**2*x*asinh(c + d*x)**4 + 4*b**4*c**2*e**2*x*asinh(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)*asinh(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)*asinh(c + d*x)/(27*d) + b**4*c*d*e**2*x**2*asinh(c + d*x)**4 + 4*b**4*c*d*e**2*x**2*asinh(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)*asinh(c + d*x)**3/9 - 16*b**4*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/27 - 8*b**4*c*e**2*asinh(c + d*x)**2/(3*d) + b**4*d**2*e**2*x**3*asinh(c + d*x)**4/3 + 4*b**4*d**2*e**2*x**3*asinh(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)*asinh(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)*asinh(c + d*x)/27 - 8*b**4*e**2*x*asinh(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)*asinh(c + d*x)**3/(9*d) + 160*b**4*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/(27*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asinh(c))**4, True))","A",0
149,1,1027,0,4.851683," ","integrate((d*e*x+c*e)*(a+b*asinh(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{asinh}{\left(c + d x \right)}}{d} + 4 a^{3} b c e x \operatorname{asinh}{\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{asinh}{\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{asinh}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} c^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c e x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{d} + 3 a^{2} b^{2} d e x^{2} \operatorname{asinh}^{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{asinh}{\left(c + d x \right)} + \frac{3 a^{2} b^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{2 d} + \frac{2 a b^{3} c^{2} e \operatorname{asinh}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} c^{2} e \operatorname{asinh}{\left(c + d x \right)}}{d} + 4 a b^{3} c e x \operatorname{asinh}^{3}{\left(c + d x \right)} + 6 a b^{3} c e x \operatorname{asinh}{\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{asinh}^{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{asinh}^{3}{\left(c + d x \right)} + 3 a b^{3} d e x^{2} \operatorname{asinh}{\left(c + d x \right)} - 3 a b^{3} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} e \operatorname{asinh}{\left(c + d x \right)}}{2 d} + \frac{b^{4} c^{2} e \operatorname{asinh}^{4}{\left(c + d x \right)}}{2 d} + \frac{3 b^{4} c^{2} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{2 d} + b^{4} c e x \operatorname{asinh}^{4}{\left(c + d x \right)} + 3 b^{4} c e x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{2 d} + \frac{b^{4} d e x^{2} \operatorname{asinh}^{4}{\left(c + d x \right)}}{2} + \frac{3 b^{4} d e x^{2} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(c + d x \right)}}{2} + \frac{b^{4} e \operatorname{asinh}^{4}{\left(c + d x \right)}}{4 d} + \frac{3 b^{4} e \operatorname{asinh}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asinh}{\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*asinh(c + d*x)/d + 4*a**3*b*c*e*x*asinh(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*asinh(c + d*x) - a**3*b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1) + a**3*b*e*asinh(c + d*x)/d + 3*a**2*b**2*c**2*e*asinh(c + d*x)**2/d + 6*a**2*b**2*c*e*x*asinh(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)*asinh(c + d*x)/d + 3*a**2*b**2*d*e*x**2*asinh(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)*asinh(c + d*x) + 3*a**2*b**2*e*asinh(c + d*x)**2/(2*d) + 2*a*b**3*c**2*e*asinh(c + d*x)**3/d + 3*a*b**3*c**2*e*asinh(c + d*x)/d + 4*a*b**3*c*e*x*asinh(c + d*x)**3 + 6*a*b**3*c*e*x*asinh(c + d*x) - 3*a*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3 + 3*a*b**3*d*e*x**2*asinh(c + d*x) - 3*a*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**3/d + 3*a*b**3*e*asinh(c + d*x)/(2*d) + b**4*c**2*e*asinh(c + d*x)**4/(2*d) + 3*b**4*c**2*e*asinh(c + d*x)**2/(2*d) + b**4*c*e*x*asinh(c + d*x)**4 + 3*b**4*c*e*x*asinh(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)*asinh(c + d*x)**3/d - 3*b**4*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/(2*d) + b**4*d*e*x**2*asinh(c + d*x)**4/2 + 3*b**4*d*e*x**2*asinh(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)*asinh(c + d*x)**3 - 3*b**4*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/2 + b**4*e*asinh(c + d*x)**4/(4*d) + 3*b**4*e*asinh(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*asinh(c))**4, True))","A",0
150,1,444,0,1.694958," ","integrate((a+b*asinh(d*x+c))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b c \operatorname{asinh}{\left(c + d x \right)}}{d} + 4 a^{3} b x \operatorname{asinh}{\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{asinh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} x \operatorname{asinh}^{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{asinh}{\left(c + d x \right)}}{d} + \frac{4 a b^{3} c \operatorname{asinh}^{3}{\left(c + d x \right)}}{d} + \frac{24 a b^{3} c \operatorname{asinh}{\left(c + d x \right)}}{d} + 4 a b^{3} x \operatorname{asinh}^{3}{\left(c + d x \right)} + 24 a b^{3} x \operatorname{asinh}{\left(c + d x \right)} - \frac{12 a b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{4}{\left(c + d x \right)}}{d} + \frac{12 b^{4} c \operatorname{asinh}^{2}{\left(c + d x \right)}}{d} + b^{4} x \operatorname{asinh}^{4}{\left(c + d x \right)} + 12 b^{4} x \operatorname{asinh}^{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{asinh}^{3}{\left(c + d x \right)}}{d} - \frac{24 b^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} + 1} \operatorname{asinh}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asinh}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*c*asinh(c + d*x)/d + 4*a**3*b*x*asinh(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*asinh(c + d*x)**2/d + 6*a**2*b**2*x*asinh(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)*asinh(c + d*x)/d + 4*a*b**3*c*asinh(c + d*x)**3/d + 24*a*b**3*c*asinh(c + d*x)/d + 4*a*b**3*x*asinh(c + d*x)**3 + 24*a*b**3*x*asinh(c + d*x) - 12*a*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(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*asinh(c + d*x)**4/d + 12*b**4*c*asinh(c + d*x)**2/d + b**4*x*asinh(c + d*x)**4 + 12*b**4*x*asinh(c + d*x)**2 + 24*b**4*x - 4*b**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)**3/d - 24*b**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 + 1)*asinh(c + d*x)/d, Ne(d, 0)), (x*(a + b*asinh(c))**4, True))","A",0
151,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4/(d*e*x+c*e),x)","\frac{\int \frac{a^{4}}{c + d x}\, dx + \int \frac{b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a^{3} b \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**4/(c + d*x), x) + Integral(b**4*asinh(c + d*x)**4/(c + d*x), x) + Integral(4*a*b**3*asinh(c + d*x)**3/(c + d*x), x) + Integral(6*a**2*b**2*asinh(c + d*x)**2/(c + d*x), x) + Integral(4*a**3*b*asinh(c + d*x)/(c + d*x), x))/e","F",0
152,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{4}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a b^{3} \operatorname{asinh}^{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{asinh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a^{3} b \operatorname{asinh}{\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*asinh(c + d*x)**4/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a*b**3*asinh(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(6*a**2*b**2*asinh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a**3*b*asinh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
153,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}^{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{asinh}^{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{asinh}{\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*asinh(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*asinh(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*asinh(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*asinh(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
154,0,0,0,0.000000," ","integrate((a+b*asinh(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{asinh}^{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{asinh}^{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{asinh}^{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{asinh}{\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*asinh(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*asinh(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*asinh(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*asinh(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
155,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m/(a+b*asinh(d*x+c)),x)","\int \frac{\left(e \left(c + d x\right)\right)^{m}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*(c + d*x))**m/(a + b*asinh(c + d*x)), x)","F",0
156,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c)),x)","e^{4} \left(\int \frac{c^{4}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a + b*asinh(c + d*x)), x) + Integral(d**4*x**4/(a + b*asinh(c + d*x)), x) + Integral(4*c*d**3*x**3/(a + b*asinh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a + b*asinh(c + d*x)), x) + Integral(4*c**3*d*x/(a + b*asinh(c + d*x)), x))","F",0
157,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c)),x)","e^{3} \left(\int \frac{c^{3}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a + b*asinh(c + d*x)), x) + Integral(d**3*x**3/(a + b*asinh(c + d*x)), x) + Integral(3*c*d**2*x**2/(a + b*asinh(c + d*x)), x) + Integral(3*c**2*d*x/(a + b*asinh(c + d*x)), x))","F",0
158,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c)),x)","e^{2} \left(\int \frac{c^{2}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a + b*asinh(c + d*x)), x) + Integral(d**2*x**2/(a + b*asinh(c + d*x)), x) + Integral(2*c*d*x/(a + b*asinh(c + d*x)), x))","F",0
159,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c)),x)","e \left(\int \frac{c}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a + b*asinh(c + d*x)), x) + Integral(d*x/(a + b*asinh(c + d*x)), x))","F",0
160,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c)),x)","\int \frac{1}{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*asinh(c + d*x)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c)),x)","\frac{\int \frac{1}{a c + a d x + b c \operatorname{asinh}{\left(c + d x \right)} + b d x \operatorname{asinh}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c + a*d*x + b*c*asinh(c + d*x) + b*d*x*asinh(c + d*x)), x)/e","F",0
162,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**2,x)","e^{4} \left(\int \frac{c^{4}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(d**4*x**4/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(4*c*d**3*x**3/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(6*c**2*d**2*x**2/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(4*c**3*d*x/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x))","F",0
163,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**2,x)","e^{3} \left(\int \frac{c^{3}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(d**3*x**3/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x))","F",0
164,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**2,x)","e^{2} \left(\int \frac{c^{2}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(d**2*x**2/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(2*c*d*x/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x))","F",0
165,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**2,x)","e \left(\int \frac{c}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} + 2 a b \operatorname{asinh}{\left(c + d x \right)} + b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x) + Integral(d*x/(a**2 + 2*a*b*asinh(c + d*x) + b**2*asinh(c + d*x)**2), x))","F",0
166,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-2), x)","F",0
167,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**2,x)","\frac{\int \frac{1}{a^{2} c + a^{2} d x + 2 a b c \operatorname{asinh}{\left(c + d x \right)} + 2 a b d x \operatorname{asinh}{\left(c + d x \right)} + b^{2} c \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{2} d x \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c + a**2*d*x + 2*a*b*c*asinh(c + d*x) + 2*a*b*d*x*asinh(c + d*x) + b**2*c*asinh(c + d*x)**2 + b**2*d*x*asinh(c + d*x)**2), x)/e","F",0
168,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**3,x)","e^{4} \left(\int \frac{c^{4}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(d**4*x**4/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(4*c*d**3*x**3/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(6*c**2*d**2*x**2/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(4*c**3*d*x/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x))","F",0
169,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**3,x)","e^{3} \left(\int \frac{c^{3}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(d**3*x**3/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x))","F",0
170,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**3,x)","e^{2} \left(\int \frac{c^{2}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(d**2*x**2/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(2*c*d*x/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x))","F",0
171,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**3,x)","e \left(\int \frac{c}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{3} + 3 a^{2} b \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x) + Integral(d*x/(a**3 + 3*a**2*b*asinh(c + d*x) + 3*a*b**2*asinh(c + d*x)**2 + b**3*asinh(c + d*x)**3), x))","F",0
172,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**3,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-3), x)","F",0
173,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**3,x)","\frac{\int \frac{1}{a^{3} c + a^{3} d x + 3 a^{2} b c \operatorname{asinh}{\left(c + d x \right)} + 3 a^{2} b d x \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} c \operatorname{asinh}^{2}{\left(c + d x \right)} + 3 a b^{2} d x \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} c \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{3} d x \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**3*c + a**3*d*x + 3*a**2*b*c*asinh(c + d*x) + 3*a**2*b*d*x*asinh(c + d*x) + 3*a*b**2*c*asinh(c + d*x)**2 + 3*a*b**2*d*x*asinh(c + d*x)**2 + b**3*c*asinh(c + d*x)**3 + b**3*d*x*asinh(c + d*x)**3), x)/e","F",0
174,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**4,x)","e^{4} \left(\int \frac{c^{4}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(d**4*x**4/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(4*c*d**3*x**3/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(6*c**2*d**2*x**2/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(4*c**3*d*x/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x))","F",0
175,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**4,x)","e^{3} \left(\int \frac{c^{3}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(d**3*x**3/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(3*c*d**2*x**2/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(3*c**2*d*x/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x))","F",0
176,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**4,x)","e^{2} \left(\int \frac{c^{2}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(d**2*x**2/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(2*c*d*x/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x))","F",0
177,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**4,x)","e \left(\int \frac{c}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{4} + 4 a^{3} b \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x) + Integral(d*x/(a**4 + 4*a**3*b*asinh(c + d*x) + 6*a**2*b**2*asinh(c + d*x)**2 + 4*a*b**3*asinh(c + d*x)**3 + b**4*asinh(c + d*x)**4), x))","F",0
178,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**4,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-4), x)","F",0
179,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**4,x)","\frac{\int \frac{1}{a^{4} c + a^{4} d x + 4 a^{3} b c \operatorname{asinh}{\left(c + d x \right)} + 4 a^{3} b d x \operatorname{asinh}{\left(c + d x \right)} + 6 a^{2} b^{2} c \operatorname{asinh}^{2}{\left(c + d x \right)} + 6 a^{2} b^{2} d x \operatorname{asinh}^{2}{\left(c + d x \right)} + 4 a b^{3} c \operatorname{asinh}^{3}{\left(c + d x \right)} + 4 a b^{3} d x \operatorname{asinh}^{3}{\left(c + d x \right)} + b^{4} c \operatorname{asinh}^{4}{\left(c + d x \right)} + b^{4} d x \operatorname{asinh}^{4}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**4*c + a**4*d*x + 4*a**3*b*c*asinh(c + d*x) + 4*a**3*b*d*x*asinh(c + d*x) + 6*a**2*b**2*c*asinh(c + d*x)**2 + 6*a**2*b**2*d*x*asinh(c + d*x)**2 + 4*a*b**3*c*asinh(c + d*x)**3 + 4*a*b**3*d*x*asinh(c + d*x)**3 + b**4*c*asinh(c + d*x)**4 + b**4*d*x*asinh(c + d*x)**4), x)/e","F",0
180,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4*(a+b*asinh(d*x+c))**(1/2),x)","e^{4} \left(\int c^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int d^{4} x^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 4 c d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 6 c^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 4 c^{3} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4*sqrt(a + b*asinh(c + d*x)), x) + Integral(d**4*x**4*sqrt(a + b*asinh(c + d*x)), x) + Integral(4*c*d**3*x**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(6*c**2*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(4*c**3*d*x*sqrt(a + b*asinh(c + d*x)), x))","F",0
181,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asinh(d*x+c))**(1/2),x)","e^{3} \left(\int c^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 3 c d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 3 c^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(d**3*x**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(3*c*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(3*c**2*d*x*sqrt(a + b*asinh(c + d*x)), x))","F",0
182,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asinh(d*x+c))**(1/2),x)","e^{2} \left(\int c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 2 c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(2*c*d*x*sqrt(a + b*asinh(c + d*x)), x))","F",0
183,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asinh(d*x+c))**(1/2),x)","e \left(\int c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c*sqrt(a + b*asinh(c + d*x)), x) + Integral(d*x*sqrt(a + b*asinh(c + d*x)), x))","F",0
184,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(1/2),x)","\int \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c + d*x)), x)","F",0
185,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(1/2)/(d*e*x+c*e),x)","\frac{\int \frac{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}{c + d x}\, dx}{e}"," ",0,"Integral(sqrt(a + b*asinh(c + d*x))/(c + d*x), x)/e","F",0
186,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4*(a+b*asinh(d*x+c))**(3/2),x)","e^{4} \left(\int a c^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a d^{4} x^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b c^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 4 a c d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 6 a c^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 4 a c^{3} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b d^{4} x^{4} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 4 b c d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 6 b c^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 4 b c^{3} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**4*(Integral(a*c**4*sqrt(a + b*asinh(c + d*x)), x) + Integral(a*d**4*x**4*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*c**4*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(4*a*c*d**3*x**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(6*a*c**2*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(4*a*c**3*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*d**4*x**4*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(4*b*c*d**3*x**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(6*b*c**2*d**2*x**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(4*b*c**3*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
187,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asinh(d*x+c))**(3/2),x)","e^{3} \left(\int a c^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b c^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 3 a c d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int 3 a c^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b d^{3} x^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 3 b c d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 3 b c^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**3*(Integral(a*c**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(a*d**3*x**3*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*c**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(3*a*c*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(3*a*c**2*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*d**3*x**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(3*b*c*d**2*x**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(3*b*c**2*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
188,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asinh(d*x+c))**(3/2),x)","e^{2} \left(\int a c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 2 a c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 2 b c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a*c**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(a*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*c**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(2*a*c*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*d**2*x**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(2*b*c*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
189,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asinh(d*x+c))**(3/2),x)","e \left(\int a c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int b d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a*c*sqrt(a + b*asinh(c + d*x)), x) + Integral(a*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(b*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
190,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(3/2),x)","\int \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(3/2)/(d*e*x+c*e),x)","\frac{\int \frac{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a*sqrt(a + b*asinh(c + d*x))/(c + d*x), x) + Integral(b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)/(c + d*x), x))/e","F",0
192,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**4*(a+b*asinh(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asinh(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asinh(d*x+c))**(5/2),x)","e^{2} \left(\int a^{2} c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b^{2} c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 2 a^{2} c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d^{2} x^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int 2 b^{2} c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}\, dx + \int 4 a b c d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a**2*c**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(a**2*d**2*x**2*sqrt(a + b*asinh(c + d*x)), x) + Integral(b**2*c**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2, x) + Integral(2*a*b*c**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(2*a**2*c*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b**2*d**2*x**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2, x) + Integral(2*a*b*d**2*x**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(2*b**2*c*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2, x) + Integral(4*a*b*c*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
195,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asinh(d*x+c))**(5/2),x)","e \left(\int a^{2} c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int a^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int b^{2} c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx + \int b^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a**2*c*sqrt(a + b*asinh(c + d*x)), x) + Integral(a**2*d*x*sqrt(a + b*asinh(c + d*x)), x) + Integral(b**2*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2, x) + Integral(2*a*b*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x) + Integral(b**2*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2, x) + Integral(2*a*b*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x), x))","F",0
196,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(5/2),x)","\int \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(5/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(5/2)/(d*e*x+c*e),x)","\frac{\int \frac{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2*sqrt(a + b*asinh(c + d*x))/(c + d*x), x) + Integral(b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)/(c + d*x), x))/e","F",0
198,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**4*(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**(7/2)/(d*e*x+c*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**(1/2),x)","e^{4} \left(\int \frac{c^{4}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{4} x^{4}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{4 c d^{3} x^{3}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{4 c^{3} d x}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**4*(Integral(c**4/sqrt(a + b*asinh(c + d*x)), x) + Integral(d**4*x**4/sqrt(a + b*asinh(c + d*x)), x) + Integral(4*c*d**3*x**3/sqrt(a + b*asinh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/sqrt(a + b*asinh(c + d*x)), x) + Integral(4*c**3*d*x/sqrt(a + b*asinh(c + d*x)), x))","F",0
205,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**(1/2),x)","e^{3} \left(\int \frac{c^{3}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{3} x^{3}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{3 c d^{2} x^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{3 c^{2} d x}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**3*(Integral(c**3/sqrt(a + b*asinh(c + d*x)), x) + Integral(d**3*x**3/sqrt(a + b*asinh(c + d*x)), x) + Integral(3*c*d**2*x**2/sqrt(a + b*asinh(c + d*x)), x) + Integral(3*c**2*d*x/sqrt(a + b*asinh(c + d*x)), x))","F",0
206,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**(1/2),x)","e^{2} \left(\int \frac{c^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{2} x^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{2 c d x}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**2*(Integral(c**2/sqrt(a + b*asinh(c + d*x)), x) + Integral(d**2*x**2/sqrt(a + b*asinh(c + d*x)), x) + Integral(2*c*d*x/sqrt(a + b*asinh(c + d*x)), x))","F",0
207,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**(1/2),x)","e \left(\int \frac{c}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx + \int \frac{d x}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e*(Integral(c/sqrt(a + b*asinh(c + d*x)), x) + Integral(d*x/sqrt(a + b*asinh(c + d*x)), x))","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asinh(c + d*x)), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**(1/2),x)","\frac{\int \frac{1}{c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}}}\, dx}{e}"," ",0,"Integral(1/(c*sqrt(a + b*asinh(c + d*x)) + d*x*sqrt(a + b*asinh(c + d*x))), x)/e","F",0
210,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**(3/2),x)","e^{4} \left(\int \frac{c^{4}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(d**4*x**4/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(4*c*d**3*x**3/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(4*c**3*d*x/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x))","F",0
211,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**(3/2),x)","e^{3} \left(\int \frac{c^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(d**3*x**3/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(3*c*d**2*x**2/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(3*c**2*d*x/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x))","F",0
212,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**(3/2),x)","e^{2} \left(\int \frac{c^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(d**2*x**2/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(2*c*d*x/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x))","F",0
213,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**(3/2),x)","e \left(\int \frac{c}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x) + Integral(d*x/(a*sqrt(a + b*asinh(c + d*x)) + b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x))","F",0
214,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-3/2), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**(3/2),x)","\frac{\int \frac{1}{a c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + a d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + b c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c*sqrt(a + b*asinh(c + d*x)) + a*d*x*sqrt(a + b*asinh(c + d*x)) + b*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)), x)/e","F",0
216,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**(5/2),x)","e^{4} \left(\int \frac{c^{4}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(d**4*x**4/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(4*c*d**3*x**3/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(6*c**2*d**2*x**2/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(4*c**3*d*x/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x))","F",0
217,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**(5/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(d**3*x**3/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x))","F",0
218,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**(5/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(d**2*x**2/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(2*c*d*x/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x))","F",0
219,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**(5/2),x)","e \left(\int \frac{c}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x) + Integral(d*x/(a**2*sqrt(a + b*asinh(c + d*x)) + 2*a*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x))","F",0
220,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-5/2), x)","F",0
221,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**(5/2),x)","\frac{\int \frac{1}{a^{2} c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + a^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 2 a b c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 2 a b d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + b^{2} c \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{2} d x \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c*sqrt(a + b*asinh(c + d*x)) + a**2*d*x*sqrt(a + b*asinh(c + d*x)) + 2*a*b*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 2*a*b*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + b**2*c*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**2*d*x*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2), x)/e","F",0
222,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asinh(d*x+c))**(7/2),x)","e^{4} \left(\int \frac{c^{4}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(d**4*x**4/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(4*c*d**3*x**3/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(6*c**2*d**2*x**2/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(4*c**3*d*x/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x))","F",0
223,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asinh(d*x+c))**(7/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(d**3*x**3/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x))","F",0
224,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asinh(d*x+c))**(7/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asinh}{\left(c + d x \right)}} \operatorname{asinh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(d**2*x**2/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x) + Integral(2*c*d*x/(a**3*sqrt(a + b*asinh(c + d*x)) + 3*a**2*b*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x) + 3*a*b**2*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**2 + b**3*sqrt(a + b*asinh(c + d*x))*asinh(c + d*x)**3), x))","F",0
225,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate(1/(a+b*asinh(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**(-7/2), x)","F",0
227,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asinh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asinh(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asinh(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asinh(d*x+c)),x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*asinh(c + d*x)), x)","F",0
231,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asinh(c + d*x)), x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))/(d*e*x+c*e)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c + d x \right)}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))/sqrt(e*(c + d*x)), x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))/(d*e*x+c*e)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))/(e*(c + d*x))**(3/2), x)","F",0
234,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))/(d*e*x+c*e)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))/(e*(c + d*x))**(5/2), x)","F",0
235,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asinh(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asinh(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asinh(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*asinh(c + d*x))**2, x)","F",0
239,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))**2, x)","F",0
240,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**2/sqrt(e*(c + d*x)), x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**2/(e*(c + d*x))**(3/2), x)","F",0
242,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**2/(e*(c + d*x))**(5/2), x)","F",0
243,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**2/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asinh(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asinh(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asinh(d*x+c))**3,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*asinh(c + d*x))**3, x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))**3, x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**3/sqrt(e*(c + d*x)), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**3/(e*(c + d*x))**(3/2), x)","F",0
250,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**3/(e*(c + d*x))**(5/2), x)","F",0
251,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**3/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asinh(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asinh(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asinh(d*x+c))**4,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*asinh(c + d*x))**4, x)","F",0
255,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))**4, x)","F",0
256,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**4/sqrt(e*(c + d*x)), x)","F",0
257,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**4/(e*(c + d*x))**(3/2), x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c + d*x))**4/(e*(c + d*x))**(5/2), x)","F",0
259,-1,0,0,0.000000," ","integrate((a+b*asinh(d*x+c))**4/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,0,0,0,0.000000," ","integrate(asinh(b*x+a)**3*(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**3, x)","F",0
261,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2*(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**2, x)","F",0
262,0,0,0,0.000000," ","integrate(asinh(b*x+a)*(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x), x)","F",0
263,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(1/2)/asinh(b*x+a),x)","\int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{\operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/asinh(a + b*x), x)","F",0
264,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(1/2)/asinh(b*x+a)**2,x)","\int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/asinh(a + b*x)**2, x)","F",0
265,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(1/2)/asinh(b*x+a)**3,x)","\int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{\operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/asinh(a + b*x)**3, x)","F",0
266,1,694,0,17.366348," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)*asinh(b*x+a)**3,x)","\begin{cases} - \frac{3 a^{4} \operatorname{asinh}^{2}{\left(a + b x \right)}}{16 b} - \frac{3 a^{3} x \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(a + b x \right)}}{32 b} - \frac{9 a^{2} b x^{2} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(a + b x \right)}}{32} - \frac{15 a^{2} \operatorname{asinh}^{2}{\left(a + b x \right)}}{16 b} - \frac{3 a b^{2} x^{3} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(a + b x \right)}}{32} - \frac{15 a x \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{8 b} + \frac{51 a \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}{\left(a + b x \right)}}{64 b} - \frac{3 b^{3} x^{4} \operatorname{asinh}^{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{asinh}^{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{asinh}{\left(a + b x \right)}}{32} - \frac{15 b x^{2} \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{8} + \frac{51 x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}{\left(a + b x \right)}}{64} + \frac{3 \operatorname{asinh}^{4}{\left(a + b x \right)}}{32 b} - \frac{51 \operatorname{asinh}^{2}{\left(a + b x \right)}}{128 b} & \text{for}\: b \neq 0 \\x \left(a^{2} + 1\right)^{\frac{3}{2}} \operatorname{asinh}^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**4*asinh(a + b*x)**2/(16*b) - 3*a**3*x*asinh(a + b*x)**2/4 - 3*a**3*x/32 + a**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**3/(4*b) + 3*a**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/(32*b) - 9*a**2*b*x**2*asinh(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)*asinh(a + b*x)**3/4 + 9*a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/32 - 15*a**2*asinh(a + b*x)**2/(16*b) - 3*a*b**2*x**3*asinh(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)*asinh(a + b*x)**3/4 + 9*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/32 - 15*a*x*asinh(a + b*x)**2/8 - 51*a*x/64 + 5*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**3/(8*b) + 51*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/(64*b) - 3*b**3*x**4*asinh(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)*asinh(a + b*x)**3/4 + 3*b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/32 - 15*b*x**2*asinh(a + b*x)**2/16 - 51*b*x**2/128 + 5*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**3/8 + 51*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/64 + 3*asinh(a + b*x)**4/(32*b) - 51*asinh(a + b*x)**2/(128*b), Ne(b, 0)), (x*(a**2 + 1)**(3/2)*asinh(a)**3, True))","A",0
267,1,568,0,10.346878," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)*asinh(b*x+a)**2,x)","\begin{cases} - \frac{a^{4} \operatorname{asinh}{\left(a + b x \right)}}{8 b} - \frac{a^{3} x \operatorname{asinh}{\left(a + b x \right)}}{2} + \frac{a^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{4} + \frac{3 a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{8 b} - \frac{a b^{2} x^{3} \operatorname{asinh}{\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{asinh}^{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{asinh}{\left(a + b x \right)}}{4} + \frac{5 a \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{8} + \frac{b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}{\left(a + b x \right)}}{8} + \frac{5 x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} \operatorname{asinh}^{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{asinh}^{3}{\left(a + b x \right)}}{8 b} - \frac{17 \operatorname{asinh}{\left(a + b x \right)}}{64 b} & \text{for}\: b \neq 0 \\x \left(a^{2} + 1\right)^{\frac{3}{2}} \operatorname{asinh}^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*asinh(a + b*x)/(8*b) - a**3*x*asinh(a + b*x)/2 + a**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/4 + 3*a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/(8*b) - a*b**2*x**3*asinh(a + b*x)/2 + 3*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/4 + 5*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/8 + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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*asinh(a + b*x)/8 + 5*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)**2/8 + 17*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/64 + asinh(a + b*x)**3/(8*b) - 17*asinh(a + b*x)/(64*b), Ne(b, 0)), (x*(a**2 + 1)**(3/2)*asinh(a)**2, True))","A",0
268,1,298,0,5.278556," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)*asinh(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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\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{asinh}{\left(a + b x \right)}}{8} + \frac{3 \operatorname{asinh}^{2}{\left(a + b x \right)}}{16 b} & \text{for}\: b \neq 0 \\x \left(a^{2} + 1\right)^{\frac{3}{2}} \operatorname{asinh}{\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)*asinh(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)*asinh(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)*asinh(a + b*x)/4 - 5*a*x/8 + 5*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(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)*asinh(a + b*x)/4 - 5*b*x**2/16 + 5*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)*asinh(a + b*x)/8 + 3*asinh(a + b*x)**2/(16*b), Ne(b, 0)), (x*(a**2 + 1)**(3/2)*asinh(a), True))","A",0
269,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)/asinh(b*x+a),x)","\int \frac{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2)/asinh(a + b*x), x)","F",0
270,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)/asinh(b*x+a)**2,x)","\int \frac{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2)/asinh(a + b*x)**2, x)","F",0
271,0,0,0,0.000000," ","integrate((b**2*x**2+2*a*b*x+a**2+1)**(3/2)/asinh(b*x+a)**3,x)","\int \frac{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\operatorname{asinh}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2)/asinh(a + b*x)**3, x)","F",0
272,1,26,0,1.197860," ","integrate(asinh(b*x+a)**3/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{4}{\left(a + b x \right)}}{4 b} & \text{for}\: b \neq 0 \\\frac{x \operatorname{asinh}^{3}{\left(a \right)}}{\sqrt{a^{2} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a + b*x)**4/(4*b), Ne(b, 0)), (x*asinh(a)**3/sqrt(a**2 + 1), True))","A",0
273,1,26,0,0.835788," ","integrate(asinh(b*x+a)**2/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\\frac{x \operatorname{asinh}^{2}{\left(a \right)}}{\sqrt{a^{2} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a + b*x)**3/(3*b), Ne(b, 0)), (x*asinh(a)**2/sqrt(a**2 + 1), True))","A",0
274,1,24,0,0.736216," ","integrate(asinh(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\\frac{x \operatorname{asinh}{\left(a \right)}}{\sqrt{a^{2} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a + b*x)**2/(2*b), Ne(b, 0)), (x*asinh(a)/sqrt(a**2 + 1), True))","A",0
275,1,22,0,1.221749," ","integrate(1/asinh(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\begin{cases} \frac{\log{\left(\operatorname{asinh}{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{a^{2} + 1} \operatorname{asinh}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(asinh(a + b*x))/b, Ne(b, 0)), (x/(sqrt(a**2 + 1)*asinh(a)), True))","A",0
276,1,26,0,1.879694," ","integrate(1/asinh(b*x+a)**2/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\begin{cases} - \frac{1}{b \operatorname{asinh}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{a^{2} + 1} \operatorname{asinh}^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*asinh(a + b*x)), Ne(b, 0)), (x/(sqrt(a**2 + 1)*asinh(a)**2), True))","A",0
277,1,29,0,2.341553," ","integrate(1/asinh(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{asinh}^{2}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{a^{2} + 1} \operatorname{asinh}^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*b*asinh(a + b*x)**2), Ne(b, 0)), (x/(sqrt(a**2 + 1)*asinh(a)**3), True))","A",0
278,0,0,0,0.000000," ","integrate(asinh(b*x+a)**3/(b**2*x**2+2*a*b*x+a**2+1)**(3/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a + b x \right)}}{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(a + b*x)**3/(a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2), x)","F",0
279,0,0,0,0.000000," ","integrate(asinh(b*x+a)**2/(b**2*x**2+2*a*b*x+a**2+1)**(3/2),x)","\int \frac{\operatorname{asinh}^{2}{\left(a + b x \right)}}{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(a + b*x)**2/(a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2), x)","F",0
280,0,0,0,0.000000," ","integrate(asinh(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(3/2),x)","\int \frac{\operatorname{asinh}{\left(a + b x \right)}}{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(a + b*x)/(a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2), x)","F",0
281,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2+1)**(3/2)/asinh(b*x+a),x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asinh}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/((a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2)*asinh(a + b*x)), x)","F",0
282,0,0,0,0.000000," ","integrate(1/(b**2*x**2+2*a*b*x+a**2+1)**(3/2)/asinh(b*x+a)**2,x)","\int \frac{1}{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/((a**2 + 2*a*b*x + b**2*x**2 + 1)**(3/2)*asinh(a + b*x)**2), x)","F",0
283,1,42,0,0.848095," ","integrate(x**3*asinh(a*x**2),x)","\begin{cases} \frac{x^{4} \operatorname{asinh}{\left(a x^{2} \right)}}{4} - \frac{x^{2} \sqrt{a^{2} x^{4} + 1}}{8 a} + \frac{\operatorname{asinh}{\left(a x^{2} \right)}}{8 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*asinh(a*x**2)/4 - x**2*sqrt(a**2*x**4 + 1)/(8*a) + asinh(a*x**2)/(8*a**2), Ne(a, 0)), (0, True))","A",0
284,0,0,0,0.000000," ","integrate(x**2*asinh(a*x**2),x)","\int x^{2} \operatorname{asinh}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**2*asinh(a*x**2), x)","F",0
285,1,27,0,0.222785," ","integrate(x*asinh(a*x**2),x)","\begin{cases} \frac{x^{2} \operatorname{asinh}{\left(a x^{2} \right)}}{2} - \frac{\sqrt{a^{2} x^{4} + 1}}{2 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*asinh(a*x**2)/2 - sqrt(a**2*x**4 + 1)/(2*a), Ne(a, 0)), (0, True))","A",0
286,0,0,0,0.000000," ","integrate(asinh(a*x**2),x)","\int \operatorname{asinh}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(asinh(a*x**2), x)","F",0
287,0,0,0,0.000000," ","integrate(asinh(a*x**2)/x,x)","\int \frac{\operatorname{asinh}{\left(a x^{2} \right)}}{x}\, dx"," ",0,"Integral(asinh(a*x**2)/x, x)","F",0
288,0,0,0,0.000000," ","integrate(asinh(a*x**2)/x**2,x)","\int \frac{\operatorname{asinh}{\left(a x^{2} \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(a*x**2)/x**2, x)","F",0
289,0,0,0,0.000000," ","integrate(asinh(a*x**2)/x**3,x)","\int \frac{\operatorname{asinh}{\left(a x^{2} \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a*x**2)/x**3, x)","F",0
290,0,0,0,0.000000," ","integrate(asinh(a*x**2)/x**4,x)","\int \frac{\operatorname{asinh}{\left(a x^{2} \right)}}{x^{4}}\, dx"," ",0,"Integral(asinh(a*x**2)/x**4, x)","F",0
291,0,0,0,0.000000," ","integrate(asinh(a*x**5)/x,x)","\int \frac{\operatorname{asinh}{\left(a x^{5} \right)}}{x}\, dx"," ",0,"Integral(asinh(a*x**5)/x, x)","F",0
292,0,0,0,0.000000," ","integrate(x**2*asinh(x**(1/2)),x)","\int x^{2} \operatorname{asinh}{\left(\sqrt{x} \right)}\, dx"," ",0,"Integral(x**2*asinh(sqrt(x)), x)","F",0
293,0,0,0,0.000000," ","integrate(x*asinh(x**(1/2)),x)","\int x \operatorname{asinh}{\left(\sqrt{x} \right)}\, dx"," ",0,"Integral(x*asinh(sqrt(x)), x)","F",0
294,1,29,0,0.302959," ","integrate(asinh(x**(1/2)),x)","- \frac{\sqrt{x} \sqrt{x + 1}}{2} + x \operatorname{asinh}{\left(\sqrt{x} \right)} + \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{2}"," ",0,"-sqrt(x)*sqrt(x + 1)/2 + x*asinh(sqrt(x)) + asinh(sqrt(x))/2","A",0
295,0,0,0,0.000000," ","integrate(asinh(x**(1/2))/x,x)","\int \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{x}\, dx"," ",0,"Integral(asinh(sqrt(x))/x, x)","F",0
296,0,0,0,0.000000," ","integrate(asinh(x**(1/2))/x**2,x)","\int \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(sqrt(x))/x**2, x)","F",0
297,0,0,0,0.000000," ","integrate(asinh(x**(1/2))/x**3,x)","\int \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(sqrt(x))/x**3, x)","F",0
298,0,0,0,0.000000," ","integrate(asinh(x**(1/2))/x**4,x)","\int \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{x^{4}}\, dx"," ",0,"Integral(asinh(sqrt(x))/x**4, x)","F",0
299,0,0,0,0.000000," ","integrate(asinh(x**(1/2))/x**5,x)","\int \frac{\operatorname{asinh}{\left(\sqrt{x} \right)}}{x^{5}}\, dx"," ",0,"Integral(asinh(sqrt(x))/x**5, x)","F",0
300,0,0,0,0.000000," ","integrate(x**2*asinh(a/x),x)","\int x^{2} \operatorname{asinh}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**2*asinh(a/x), x)","F",0
301,0,0,0,0.000000," ","integrate(x*asinh(a/x),x)","\int x \operatorname{asinh}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x*asinh(a/x), x)","F",0
302,0,0,0,0.000000," ","integrate(asinh(a/x),x)","\int \operatorname{asinh}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(asinh(a/x), x)","F",0
303,0,0,0,0.000000," ","integrate(asinh(a/x)/x,x)","\int \frac{\operatorname{asinh}{\left(\frac{a}{x} \right)}}{x}\, dx"," ",0,"Integral(asinh(a/x)/x, x)","F",0
304,1,20,0,1.927268," ","integrate(asinh(a/x)/x**2,x)","\begin{cases} - \frac{\operatorname{asinh}{\left(\frac{a}{x} \right)}}{x} + \frac{\sqrt{\frac{a^{2}}{x^{2}} + 1}}{a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-asinh(a/x)/x + sqrt(a**2/x**2 + 1)/a, Ne(a, 0)), (0, True))","A",0
305,0,0,0,0.000000," ","integrate(asinh(a/x)/x**3,x)","\int \frac{\operatorname{asinh}{\left(\frac{a}{x} \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a/x)/x**3, x)","F",0
306,0,0,0,0.000000," ","integrate(asinh(a/x)/x**4,x)","\int \frac{\operatorname{asinh}{\left(\frac{a}{x} \right)}}{x^{4}}\, dx"," ",0,"Integral(asinh(a/x)/x**4, x)","F",0
307,0,0,0,0.000000," ","integrate(x**m*asinh(a*x**n),x)","\int x^{m} \operatorname{asinh}{\left(a x^{n} \right)}\, dx"," ",0,"Integral(x**m*asinh(a*x**n), x)","F",0
308,0,0,0,0.000000," ","integrate(x**2*asinh(a*x**n),x)","\int x^{2} \operatorname{asinh}{\left(a x^{n} \right)}\, dx"," ",0,"Integral(x**2*asinh(a*x**n), x)","F",0
309,0,0,0,0.000000," ","integrate(x*asinh(a*x**n),x)","\int x \operatorname{asinh}{\left(a x^{n} \right)}\, dx"," ",0,"Integral(x*asinh(a*x**n), x)","F",0
310,0,0,0,0.000000," ","integrate(asinh(a*x**n),x)","\int \operatorname{asinh}{\left(a x^{n} \right)}\, dx"," ",0,"Integral(asinh(a*x**n), x)","F",0
311,0,0,0,0.000000," ","integrate(asinh(a*x**n)/x,x)","\int \frac{\operatorname{asinh}{\left(a x^{n} \right)}}{x}\, dx"," ",0,"Integral(asinh(a*x**n)/x, x)","F",0
312,0,0,0,0.000000," ","integrate(asinh(a*x**n)/x**2,x)","\int \frac{\operatorname{asinh}{\left(a x^{n} \right)}}{x^{2}}\, dx"," ",0,"Integral(asinh(a*x**n)/x**2, x)","F",0
313,0,0,0,0.000000," ","integrate(asinh(a*x**n)/x**3,x)","\int \frac{\operatorname{asinh}{\left(a x^{n} \right)}}{x^{3}}\, dx"," ",0,"Integral(asinh(a*x**n)/x**3, x)","F",0
314,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**4,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
315,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
316,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
317,-2,0,0,0.000000," ","integrate(a+b*asinh(I+d*x**2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
318,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
319,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
320,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
321,-2,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**4,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
322,-2,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
323,-2,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
324,-2,0,0,0.000000," ","integrate(a+b*asinh(-I+d*x**2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
325,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
326,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
327,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
328,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
329,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
330,-2,0,0,0.000000," ","integrate((a+b*asinh(I+d*x**2))**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
331,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
332,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
333,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
334,-1,0,0,0.000000," ","integrate(1/(a+b*asinh(I+d*x**2))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-2,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
337,-2,0,0,0.000000," ","integrate((a+b*asinh(-I+d*x**2))**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
338,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
339,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
340,-2,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
341,-1,0,0,0.000000," ","integrate(1/(a+b*asinh(-I+d*x**2))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate((a+b*asinh((-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
343,0,0,0,0.000000," ","integrate((a+b*asinh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**3/(-c**2*x**2+1),x)","- \int \frac{a^{3}}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{3} \operatorname{asinh}^{3}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{3 a b^{2} \operatorname{asinh}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{3 a^{2} b \operatorname{asinh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a**3/(c**2*x**2 - 1), x) - Integral(b**3*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))**3/(c**2*x**2 - 1), x) - Integral(3*a*b**2*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))**2/(c**2*x**2 - 1), x) - Integral(3*a**2*b*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
344,0,0,0,0.000000," ","integrate((a+b*asinh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2/(-c**2*x**2+1),x)","- \int \frac{a^{2}}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{2} \operatorname{asinh}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{2 a b \operatorname{asinh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a**2/(c**2*x**2 - 1), x) - Integral(b**2*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))**2/(c**2*x**2 - 1), x) - Integral(2*a*b*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
345,0,0,0,0.000000," ","integrate((a+b*asinh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))/(-c**2*x**2+1),x)","- \int \frac{a}{c^{2} x^{2} - 1}\, dx - \int \frac{b \operatorname{asinh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a/(c**2*x**2 - 1), x) - Integral(b*asinh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
346,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*asinh((-c*x+1)**(1/2)/(c*x+1)**(1/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*asinh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,0,0,0,0.000000," ","integrate(asinh(c*exp(b*x+a)),x)","\int \operatorname{asinh}{\left(c e^{a + b x} \right)}\, dx"," ",0,"Integral(asinh(c*exp(a + b*x)), x)","F",0
349,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))*x**3,x)","\int x^{3} \left(a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}\right)\, dx"," ",0,"Integral(x**3*(a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
350,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))*x**2,x)","\int x^{2} \left(a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}\right)\, dx"," ",0,"Integral(x**2*(a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
351,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))*x,x)","\int x \left(a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}\right)\, dx"," ",0,"Integral(x*(a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
352,0,0,0,0.000000," ","integrate(b*x+a+(1+(b*x+a)**2)**(1/2),x)","\int \left(a + b x + \sqrt{\left(a + b x\right)^{2} + 1}\right)\, dx"," ",0,"Integral(a + b*x + sqrt((a + b*x)**2 + 1), x)","F",0
353,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))/x,x)","\int \frac{a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{x}\, dx"," ",0,"Integral((a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x, x)","F",0
354,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))/x**2,x)","\int \frac{a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{x^{2}}\, dx"," ",0,"Integral((a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x**2, x)","F",0
355,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))/x**3,x)","\int \frac{a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{x^{3}}\, dx"," ",0,"Integral((a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x**3, x)","F",0
356,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))/x**4,x)","\int \frac{a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{x^{4}}\, dx"," ",0,"Integral((a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x**4, x)","F",0
357,0,0,0,0.000000," ","integrate((b*x+a+(1+(b*x+a)**2)**(1/2))/x**5,x)","\int \frac{a + b x + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{x^{5}}\, dx"," ",0,"Integral((a + b*x + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x**5, x)","F",0
358,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2)*x**3,x)","\int x^{3} e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**3*exp(asinh(a + b*x)**2), x)","F",0
359,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2)*x**2,x)","\int x^{2} e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2*exp(asinh(a + b*x)**2), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2)*x,x)","\int x e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*exp(asinh(a + b*x)**2), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2),x)","\int e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(exp(asinh(a + b*x)**2), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2)/x,x)","\int \frac{e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(exp(asinh(a + b*x)**2)/x, x)","F",0
363,0,0,0,0.000000," ","integrate(exp(asinh(b*x+a)**2)/x**2,x)","\int \frac{e^{\operatorname{asinh}^{2}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(asinh(a + b*x)**2)/x**2, x)","F",0
364,0,0,0,0.000000," ","integrate(asinh(b*x+a)/(a*d/b+d*x),x)","\frac{b \int \frac{\operatorname{asinh}{\left(a + b x \right)}}{a + b x}\, dx}{d}"," ",0,"b*Integral(asinh(a + b*x)/(a + b*x), x)/d","F",0
365,0,0,0,0.000000," ","integrate(x/asinh(x)/(x**2+1)**(1/2),x)","\int \frac{x}{\sqrt{x^{2} + 1} \operatorname{asinh}{\left(x \right)}}\, dx"," ",0,"Integral(x/(sqrt(x**2 + 1)*asinh(x)), x)","F",0
366,1,61,0,0.847251," ","integrate(x**3*asinh(b*x**4+a),x)","\begin{cases} \frac{a \operatorname{asinh}{\left(a + b x^{4} \right)}}{4 b} + \frac{x^{4} \operatorname{asinh}{\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{asinh}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asinh(a + b*x**4)/(4*b) + x**4*asinh(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*asinh(a)/4, True))","A",0
367,1,76,0,71.047752," ","integrate(x**(-1+n)*asinh(a+b*x**n),x)","\begin{cases} \log{\left(x \right)} \operatorname{asinh}{\left(a \right)} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{n} \operatorname{asinh}{\left(a \right)}}{n} & \text{for}\: b = 0 \\\log{\left(x \right)} \operatorname{asinh}{\left(a + b \right)} & \text{for}\: n = 0 \\\frac{a \operatorname{asinh}{\left(a + b x^{n} \right)}}{b n} + \frac{x^{n} \operatorname{asinh}{\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)*asinh(a), Eq(b, 0) & Eq(n, 0)), (x**n*asinh(a)/n, Eq(b, 0)), (log(x)*asinh(a + b), Eq(n, 0)), (a*asinh(a + b*x**n)/(b*n) + x**n*asinh(a + b*x**n)/n - sqrt(a**2 + 2*a*b*x**n + b**2*x**(2*n) + 1)/(b*n), True))","A",0
368,0,0,0,0.000000," ","integrate(asinh(c/(b*x+a)),x)","\int \operatorname{asinh}{\left(\frac{c}{a + b x} \right)}\, dx"," ",0,"Integral(asinh(c/(a + b*x)), x)","F",0
369,0,0,0,0.000000," ","integrate(x/asinh(sinh(x)),x)","\int \frac{x}{\operatorname{asinh}{\left(\sinh{\left(x \right)} \right)}}\, dx"," ",0,"Integral(x/asinh(sinh(x)), x)","F",0
370,0,0,0,0.000000," ","integrate(asinh((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 \\- i x \left(\frac{i \pi}{2}\right)^{n} & \text{for}\: b = 0 \\\int \frac{1}{\sqrt{b x^{2} - 1} \operatorname{asinh}{\left(\sqrt{b x^{2} - 1} \right)}}\, dx & \text{for}\: n = -1 \\\frac{\sqrt{b} \sqrt{x^{2}} \operatorname{asinh}{\left(\sqrt{b x^{2} - 1} \right)} \operatorname{asinh}^{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)), (-I*x*(I*pi/2)**n, Eq(b, 0)), (Integral(1/(sqrt(b*x**2 - 1)*asinh(sqrt(b*x**2 - 1))), x), Eq(n, -1)), (sqrt(b)*sqrt(x**2)*asinh(sqrt(b*x**2 - 1))*asinh(sqrt(b*x**2 - 1))**n/(b*n*x + b*x), True))","F",0
371,0,0,0,0.000000," ","integrate(1/asinh((b*x**2-1)**(1/2))/(b*x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} - 1} \operatorname{asinh}{\left(\sqrt{b x^{2} - 1} \right)}}\, dx"," ",0,"Integral(1/(sqrt(b*x**2 - 1)*asinh(sqrt(b*x**2 - 1))), x)","F",0
