1,1,151,0,5.683966," ","integrate(x**4*(c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{2} d x^{7}}{7} + \frac{a d x^{5}}{5} + \frac{b c^{2} d x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{b c d x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{b d x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{19 b d x^{4} \sqrt{c^{2} x^{2} + 1}}{1225 c} + \frac{76 b d x^{2} \sqrt{c^{2} x^{2} + 1}}{3675 c^{3}} - \frac{152 b d \sqrt{c^{2} x^{2} + 1}}{3675 c^{5}} & \text{for}\: c \neq 0 \\\frac{a d x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d*x**7/7 + a*d*x**5/5 + b*c**2*d*x**7*asinh(c*x)/7 - b*c*d*x**6*sqrt(c**2*x**2 + 1)/49 + b*d*x**5*asinh(c*x)/5 - 19*b*d*x**4*sqrt(c**2*x**2 + 1)/(1225*c) + 76*b*d*x**2*sqrt(c**2*x**2 + 1)/(3675*c**3) - 152*b*d*sqrt(c**2*x**2 + 1)/(3675*c**5), Ne(c, 0)), (a*d*x**5/5, True))","A",0
2,1,138,0,3.758120," ","integrate(x**3*(c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{2} d x^{6}}{6} + \frac{a d x^{4}}{4} + \frac{b c^{2} d x^{6} \operatorname{asinh}{\left(c x \right)}}{6} - \frac{b c d x^{5} \sqrt{c^{2} x^{2} + 1}}{36} + \frac{b d x^{4} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{b d x^{3} \sqrt{c^{2} x^{2} + 1}}{36 c} + \frac{b d x \sqrt{c^{2} x^{2} + 1}}{24 c^{3}} - \frac{b d \operatorname{asinh}{\left(c x \right)}}{24 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d*x**6/6 + a*d*x**4/4 + b*c**2*d*x**6*asinh(c*x)/6 - b*c*d*x**5*sqrt(c**2*x**2 + 1)/36 + b*d*x**4*asinh(c*x)/4 - b*d*x**3*sqrt(c**2*x**2 + 1)/(36*c) + b*d*x*sqrt(c**2*x**2 + 1)/(24*c**3) - b*d*asinh(c*x)/(24*c**4), Ne(c, 0)), (a*d*x**4/4, True))","A",0
3,1,126,0,2.019781," ","integrate(x**2*(c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{2} d x^{5}}{5} + \frac{a d x^{3}}{3} + \frac{b c^{2} d x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{b c d x^{4} \sqrt{c^{2} x^{2} + 1}}{25} + \frac{b d x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{13 b d x^{2} \sqrt{c^{2} x^{2} + 1}}{225 c} + \frac{26 b d \sqrt{c^{2} x^{2} + 1}}{225 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d*x**5/5 + a*d*x**3/3 + b*c**2*d*x**5*asinh(c*x)/5 - b*c*d*x**4*sqrt(c**2*x**2 + 1)/25 + b*d*x**3*asinh(c*x)/3 - 13*b*d*x**2*sqrt(c**2*x**2 + 1)/(225*c) + 26*b*d*sqrt(c**2*x**2 + 1)/(225*c**3), Ne(c, 0)), (a*d*x**3/3, True))","A",0
4,1,117,0,1.156564," ","integrate(x*(c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{2} d x^{4}}{4} + \frac{a d x^{2}}{2} + \frac{b c^{2} d x^{4} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{b c d x^{3} \sqrt{c^{2} x^{2} + 1}}{16} + \frac{b d x^{2} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{5 b d x \sqrt{c^{2} x^{2} + 1}}{32 c} + \frac{5 b d \operatorname{asinh}{\left(c x \right)}}{32 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d*x**4/4 + a*d*x**2/2 + b*c**2*d*x**4*asinh(c*x)/4 - b*c*d*x**3*sqrt(c**2*x**2 + 1)/16 + b*d*x**2*asinh(c*x)/2 - 5*b*d*x*sqrt(c**2*x**2 + 1)/(32*c) + 5*b*d*asinh(c*x)/(32*c**2), Ne(c, 0)), (a*d*x**2/2, True))","A",0
5,1,90,0,0.521385," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{2} d x^{3}}{3} + a d x + \frac{b c^{2} d x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{b c d x^{2} \sqrt{c^{2} x^{2} + 1}}{9} + b d x \operatorname{asinh}{\left(c x \right)} - \frac{7 b d \sqrt{c^{2} x^{2} + 1}}{9 c} & \text{for}\: c \neq 0 \\a d x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d*x**3/3 + a*d*x + b*c**2*d*x**3*asinh(c*x)/3 - b*c*d*x**2*sqrt(c**2*x**2 + 1)/9 + b*d*x*asinh(c*x) - 7*b*d*sqrt(c**2*x**2 + 1)/(9*c), Ne(c, 0)), (a*d*x, True))","A",0
6,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))/x,x)","d \left(\int \frac{a}{x}\, dx + \int a c^{2} x\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a/x, x) + Integral(a*c**2*x, x) + Integral(b*asinh(c*x)/x, x) + Integral(b*c**2*x*asinh(c*x), x))","F",0
7,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))/x**2,x)","d \left(\int a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d*(Integral(a*c**2, x) + Integral(a/x**2, x) + Integral(b*c**2*asinh(c*x), x) + Integral(b*asinh(c*x)/x**2, x))","F",0
8,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))/x**3,x)","d \left(\int \frac{a}{x^{3}}\, dx + \int \frac{a c^{2}}{x}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a/x**3, x) + Integral(a*c**2/x, x) + Integral(b*asinh(c*x)/x**3, x) + Integral(b*c**2*asinh(c*x)/x, x))","F",0
9,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))/x**4,x)","d \left(\int \frac{a}{x^{4}}\, dx + \int \frac{a c^{2}}{x^{2}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d*(Integral(a/x**4, x) + Integral(a*c**2/x**2, x) + Integral(b*asinh(c*x)/x**4, x) + Integral(b*c**2*asinh(c*x)/x**2, x))","F",0
10,1,230,0,16.103910," ","integrate(x**4*(c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{2} x^{9}}{9} + \frac{2 a c^{2} d^{2} x^{7}}{7} + \frac{a d^{2} x^{5}}{5} + \frac{b c^{4} d^{2} x^{9} \operatorname{asinh}{\left(c x \right)}}{9} - \frac{b c^{3} d^{2} x^{8} \sqrt{c^{2} x^{2} + 1}}{81} + \frac{2 b c^{2} d^{2} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{106 b c d^{2} x^{6} \sqrt{c^{2} x^{2} + 1}}{3969} + \frac{b d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{263 b d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{33075 c} + \frac{1052 b d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c^{3}} - \frac{2104 b d^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c^{5}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**2*x**9/9 + 2*a*c**2*d**2*x**7/7 + a*d**2*x**5/5 + b*c**4*d**2*x**9*asinh(c*x)/9 - b*c**3*d**2*x**8*sqrt(c**2*x**2 + 1)/81 + 2*b*c**2*d**2*x**7*asinh(c*x)/7 - 106*b*c*d**2*x**6*sqrt(c**2*x**2 + 1)/3969 + b*d**2*x**5*asinh(c*x)/5 - 263*b*d**2*x**4*sqrt(c**2*x**2 + 1)/(33075*c) + 1052*b*d**2*x**2*sqrt(c**2*x**2 + 1)/(99225*c**3) - 2104*b*d**2*sqrt(c**2*x**2 + 1)/(99225*c**5), Ne(c, 0)), (a*d**2*x**5/5, True))","A",0
11,1,218,0,10.995933," ","integrate(x**3*(c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{2} x^{8}}{8} + \frac{a c^{2} d^{2} x^{6}}{3} + \frac{a d^{2} x^{4}}{4} + \frac{b c^{4} d^{2} x^{8} \operatorname{asinh}{\left(c x \right)}}{8} - \frac{b c^{3} d^{2} x^{7} \sqrt{c^{2} x^{2} + 1}}{64} + \frac{b c^{2} d^{2} x^{6} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{43 b c d^{2} x^{5} \sqrt{c^{2} x^{2} + 1}}{1152} + \frac{b d^{2} x^{4} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{73 b d^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{4608 c} + \frac{73 b d^{2} x \sqrt{c^{2} x^{2} + 1}}{3072 c^{3}} - \frac{73 b d^{2} \operatorname{asinh}{\left(c x \right)}}{3072 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**2*x**8/8 + a*c**2*d**2*x**6/3 + a*d**2*x**4/4 + b*c**4*d**2*x**8*asinh(c*x)/8 - b*c**3*d**2*x**7*sqrt(c**2*x**2 + 1)/64 + b*c**2*d**2*x**6*asinh(c*x)/3 - 43*b*c*d**2*x**5*sqrt(c**2*x**2 + 1)/1152 + b*d**2*x**4*asinh(c*x)/4 - 73*b*d**2*x**3*sqrt(c**2*x**2 + 1)/(4608*c) + 73*b*d**2*x*sqrt(c**2*x**2 + 1)/(3072*c**3) - 73*b*d**2*asinh(c*x)/(3072*c**4), Ne(c, 0)), (a*d**2*x**4/4, True))","A",0
12,1,202,0,6.138461," ","integrate(x**2*(c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{2} x^{7}}{7} + \frac{2 a c^{2} d^{2} x^{5}}{5} + \frac{a d^{2} x^{3}}{3} + \frac{b c^{4} d^{2} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{b c^{3} d^{2} x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{2 b c^{2} d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{68 b c d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{1225} + \frac{b d^{2} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{409 b d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{11025 c} + \frac{818 b d^{2} \sqrt{c^{2} x^{2} + 1}}{11025 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**2*x**7/7 + 2*a*c**2*d**2*x**5/5 + a*d**2*x**3/3 + b*c**4*d**2*x**7*asinh(c*x)/7 - b*c**3*d**2*x**6*sqrt(c**2*x**2 + 1)/49 + 2*b*c**2*d**2*x**5*asinh(c*x)/5 - 68*b*c*d**2*x**4*sqrt(c**2*x**2 + 1)/1225 + b*d**2*x**3*asinh(c*x)/3 - 409*b*d**2*x**2*sqrt(c**2*x**2 + 1)/(11025*c) + 818*b*d**2*sqrt(c**2*x**2 + 1)/(11025*c**3), Ne(c, 0)), (a*d**2*x**3/3, True))","A",0
13,1,190,0,4.162317," ","integrate(x*(c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{2} x^{6}}{6} + \frac{a c^{2} d^{2} x^{4}}{2} + \frac{a d^{2} x^{2}}{2} + \frac{b c^{4} d^{2} x^{6} \operatorname{asinh}{\left(c x \right)}}{6} - \frac{b c^{3} d^{2} x^{5} \sqrt{c^{2} x^{2} + 1}}{36} + \frac{b c^{2} d^{2} x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{13 b c d^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{144} + \frac{b d^{2} x^{2} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{11 b d^{2} x \sqrt{c^{2} x^{2} + 1}}{96 c} + \frac{11 b d^{2} \operatorname{asinh}{\left(c x \right)}}{96 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**2*x**6/6 + a*c**2*d**2*x**4/2 + a*d**2*x**2/2 + b*c**4*d**2*x**6*asinh(c*x)/6 - b*c**3*d**2*x**5*sqrt(c**2*x**2 + 1)/36 + b*c**2*d**2*x**4*asinh(c*x)/2 - 13*b*c*d**2*x**3*sqrt(c**2*x**2 + 1)/144 + b*d**2*x**2*asinh(c*x)/2 - 11*b*d**2*x*sqrt(c**2*x**2 + 1)/(96*c) + 11*b*d**2*asinh(c*x)/(96*c**2), Ne(c, 0)), (a*d**2*x**2/2, True))","A",0
14,1,165,0,2.258784," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{2} x^{5}}{5} + \frac{2 a c^{2} d^{2} x^{3}}{3} + a d^{2} x + \frac{b c^{4} d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{b c^{3} d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25} + \frac{2 b c^{2} d^{2} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{38 b c d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{225} + b d^{2} x \operatorname{asinh}{\left(c x \right)} - \frac{149 b d^{2} \sqrt{c^{2} x^{2} + 1}}{225 c} & \text{for}\: c \neq 0 \\a d^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**2*x**5/5 + 2*a*c**2*d**2*x**3/3 + a*d**2*x + b*c**4*d**2*x**5*asinh(c*x)/5 - b*c**3*d**2*x**4*sqrt(c**2*x**2 + 1)/25 + 2*b*c**2*d**2*x**3*asinh(c*x)/3 - 38*b*c*d**2*x**2*sqrt(c**2*x**2 + 1)/225 + b*d**2*x*asinh(c*x) - 149*b*d**2*sqrt(c**2*x**2 + 1)/(225*c), Ne(c, 0)), (a*d**2*x, True))","A",0
15,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))/x,x)","d^{2} \left(\int \frac{a}{x}\, dx + \int 2 a c^{2} x\, dx + \int a c^{4} x^{3}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 2 b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{4} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a/x, x) + Integral(2*a*c**2*x, x) + Integral(a*c**4*x**3, x) + Integral(b*asinh(c*x)/x, x) + Integral(2*b*c**2*x*asinh(c*x), x) + Integral(b*c**4*x**3*asinh(c*x), x))","F",0
16,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))/x**2,x)","d^{2} \left(\int 2 a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int a c^{4} x^{2}\, dx + \int 2 b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int b c^{4} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(2*a*c**2, x) + Integral(a/x**2, x) + Integral(a*c**4*x**2, x) + Integral(2*b*c**2*asinh(c*x), x) + Integral(b*asinh(c*x)/x**2, x) + Integral(b*c**4*x**2*asinh(c*x), x))","F",0
17,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))/x**3,x)","d^{2} \left(\int \frac{a}{x^{3}}\, dx + \int \frac{2 a c^{2}}{x}\, dx + \int a c^{4} x\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int b c^{4} x \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a/x**3, x) + Integral(2*a*c**2/x, x) + Integral(a*c**4*x, x) + Integral(b*asinh(c*x)/x**3, x) + Integral(2*b*c**2*asinh(c*x)/x, x) + Integral(b*c**4*x*asinh(c*x), x))","F",0
18,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))/x**4,x)","d^{2} \left(\int a c^{4}\, dx + \int \frac{a}{x^{4}}\, dx + \int \frac{2 a c^{2}}{x^{2}}\, dx + \int b c^{4} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d**2*(Integral(a*c**4, x) + Integral(a/x**4, x) + Integral(2*a*c**2/x**2, x) + Integral(b*c**4*asinh(c*x), x) + Integral(b*asinh(c*x)/x**4, x) + Integral(2*b*c**2*asinh(c*x)/x**2, x))","F",0
19,1,289,0,39.152892," ","integrate(x**4*(c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{6} d^{3} x^{11}}{11} + \frac{a c^{4} d^{3} x^{9}}{3} + \frac{3 a c^{2} d^{3} x^{7}}{7} + \frac{a d^{3} x^{5}}{5} + \frac{b c^{6} d^{3} x^{11} \operatorname{asinh}{\left(c x \right)}}{11} - \frac{b c^{5} d^{3} x^{10} \sqrt{c^{2} x^{2} + 1}}{121} + \frac{b c^{4} d^{3} x^{9} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{91 b c^{3} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1}}{3267} + \frac{3 b c^{2} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{4705 b c d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{160083} + \frac{b d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{6311 b d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{1334025 c} + \frac{25244 b d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{4002075 c^{3}} - \frac{50488 b d^{3} \sqrt{c^{2} x^{2} + 1}}{4002075 c^{5}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**6*d**3*x**11/11 + a*c**4*d**3*x**9/3 + 3*a*c**2*d**3*x**7/7 + a*d**3*x**5/5 + b*c**6*d**3*x**11*asinh(c*x)/11 - b*c**5*d**3*x**10*sqrt(c**2*x**2 + 1)/121 + b*c**4*d**3*x**9*asinh(c*x)/3 - 91*b*c**3*d**3*x**8*sqrt(c**2*x**2 + 1)/3267 + 3*b*c**2*d**3*x**7*asinh(c*x)/7 - 4705*b*c*d**3*x**6*sqrt(c**2*x**2 + 1)/160083 + b*d**3*x**5*asinh(c*x)/5 - 6311*b*d**3*x**4*sqrt(c**2*x**2 + 1)/(1334025*c) + 25244*b*d**3*x**2*sqrt(c**2*x**2 + 1)/(4002075*c**3) - 50488*b*d**3*sqrt(c**2*x**2 + 1)/(4002075*c**5), Ne(c, 0)), (a*d**3*x**5/5, True))","A",0
20,1,280,0,28.239950," ","integrate(x**3*(c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{6} d^{3} x^{10}}{10} + \frac{3 a c^{4} d^{3} x^{8}}{8} + \frac{a c^{2} d^{3} x^{6}}{2} + \frac{a d^{3} x^{4}}{4} + \frac{b c^{6} d^{3} x^{10} \operatorname{asinh}{\left(c x \right)}}{10} - \frac{b c^{5} d^{3} x^{9} \sqrt{c^{2} x^{2} + 1}}{100} + \frac{3 b c^{4} d^{3} x^{8} \operatorname{asinh}{\left(c x \right)}}{8} - \frac{57 b c^{3} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1}}{1600} + \frac{b c^{2} d^{3} x^{6} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{401 b c d^{3} x^{5} \sqrt{c^{2} x^{2} + 1}}{9600} + \frac{b d^{3} x^{4} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{79 b d^{3} x^{3} \sqrt{c^{2} x^{2} + 1}}{7680 c} + \frac{79 b d^{3} x \sqrt{c^{2} x^{2} + 1}}{5120 c^{3}} - \frac{79 b d^{3} \operatorname{asinh}{\left(c x \right)}}{5120 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**6*d**3*x**10/10 + 3*a*c**4*d**3*x**8/8 + a*c**2*d**3*x**6/2 + a*d**3*x**4/4 + b*c**6*d**3*x**10*asinh(c*x)/10 - b*c**5*d**3*x**9*sqrt(c**2*x**2 + 1)/100 + 3*b*c**4*d**3*x**8*asinh(c*x)/8 - 57*b*c**3*d**3*x**7*sqrt(c**2*x**2 + 1)/1600 + b*c**2*d**3*x**6*asinh(c*x)/2 - 401*b*c*d**3*x**5*sqrt(c**2*x**2 + 1)/9600 + b*d**3*x**4*asinh(c*x)/4 - 79*b*d**3*x**3*sqrt(c**2*x**2 + 1)/(7680*c) + 79*b*d**3*x*sqrt(c**2*x**2 + 1)/(5120*c**3) - 79*b*d**3*asinh(c*x)/(5120*c**4), Ne(c, 0)), (a*d**3*x**4/4, True))","A",0
21,1,265,0,16.746258," ","integrate(x**2*(c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{6} d^{3} x^{9}}{9} + \frac{3 a c^{4} d^{3} x^{7}}{7} + \frac{3 a c^{2} d^{3} x^{5}}{5} + \frac{a d^{3} x^{3}}{3} + \frac{b c^{6} d^{3} x^{9} \operatorname{asinh}{\left(c x \right)}}{9} - \frac{b c^{5} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1}}{81} + \frac{3 b c^{4} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{187 b c^{3} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{3969} + \frac{3 b c^{2} d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{2099 b c d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{33075} + \frac{b d^{3} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{2629 b d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c} + \frac{5258 b d^{3} \sqrt{c^{2} x^{2} + 1}}{99225 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**6*d**3*x**9/9 + 3*a*c**4*d**3*x**7/7 + 3*a*c**2*d**3*x**5/5 + a*d**3*x**3/3 + b*c**6*d**3*x**9*asinh(c*x)/9 - b*c**5*d**3*x**8*sqrt(c**2*x**2 + 1)/81 + 3*b*c**4*d**3*x**7*asinh(c*x)/7 - 187*b*c**3*d**3*x**6*sqrt(c**2*x**2 + 1)/3969 + 3*b*c**2*d**3*x**5*asinh(c*x)/5 - 2099*b*c*d**3*x**4*sqrt(c**2*x**2 + 1)/33075 + b*d**3*x**3*asinh(c*x)/3 - 2629*b*d**3*x**2*sqrt(c**2*x**2 + 1)/(99225*c) + 5258*b*d**3*sqrt(c**2*x**2 + 1)/(99225*c**3), Ne(c, 0)), (a*d**3*x**3/3, True))","A",0
22,1,253,0,11.421915," ","integrate(x*(c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{6} d^{3} x^{8}}{8} + \frac{a c^{4} d^{3} x^{6}}{2} + \frac{3 a c^{2} d^{3} x^{4}}{4} + \frac{a d^{3} x^{2}}{2} + \frac{b c^{6} d^{3} x^{8} \operatorname{asinh}{\left(c x \right)}}{8} - \frac{b c^{5} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1}}{64} + \frac{b c^{4} d^{3} x^{6} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{25 b c^{3} d^{3} x^{5} \sqrt{c^{2} x^{2} + 1}}{384} + \frac{3 b c^{2} d^{3} x^{4} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{163 b c d^{3} x^{3} \sqrt{c^{2} x^{2} + 1}}{1536} + \frac{b d^{3} x^{2} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{93 b d^{3} x \sqrt{c^{2} x^{2} + 1}}{1024 c} + \frac{93 b d^{3} \operatorname{asinh}{\left(c x \right)}}{1024 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**6*d**3*x**8/8 + a*c**4*d**3*x**6/2 + 3*a*c**2*d**3*x**4/4 + a*d**3*x**2/2 + b*c**6*d**3*x**8*asinh(c*x)/8 - b*c**5*d**3*x**7*sqrt(c**2*x**2 + 1)/64 + b*c**4*d**3*x**6*asinh(c*x)/2 - 25*b*c**3*d**3*x**5*sqrt(c**2*x**2 + 1)/384 + 3*b*c**2*d**3*x**4*asinh(c*x)/4 - 163*b*c*d**3*x**3*sqrt(c**2*x**2 + 1)/1536 + b*d**3*x**2*asinh(c*x)/2 - 93*b*d**3*x*sqrt(c**2*x**2 + 1)/(1024*c) + 93*b*d**3*asinh(c*x)/(1024*c**2), Ne(c, 0)), (a*d**3*x**2/2, True))","A",0
23,1,221,0,6.234962," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} \frac{a c^{6} d^{3} x^{7}}{7} + \frac{3 a c^{4} d^{3} x^{5}}{5} + a c^{2} d^{3} x^{3} + a d^{3} x + \frac{b c^{6} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{b c^{5} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{3 b c^{4} d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{117 b c^{3} d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{1225} + b c^{2} d^{3} x^{3} \operatorname{asinh}{\left(c x \right)} - \frac{757 b c d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{3675} + b d^{3} x \operatorname{asinh}{\left(c x \right)} - \frac{2161 b d^{3} \sqrt{c^{2} x^{2} + 1}}{3675 c} & \text{for}\: c \neq 0 \\a d^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**6*d**3*x**7/7 + 3*a*c**4*d**3*x**5/5 + a*c**2*d**3*x**3 + a*d**3*x + b*c**6*d**3*x**7*asinh(c*x)/7 - b*c**5*d**3*x**6*sqrt(c**2*x**2 + 1)/49 + 3*b*c**4*d**3*x**5*asinh(c*x)/5 - 117*b*c**3*d**3*x**4*sqrt(c**2*x**2 + 1)/1225 + b*c**2*d**3*x**3*asinh(c*x) - 757*b*c*d**3*x**2*sqrt(c**2*x**2 + 1)/3675 + b*d**3*x*asinh(c*x) - 2161*b*d**3*sqrt(c**2*x**2 + 1)/(3675*c), Ne(c, 0)), (a*d**3*x, True))","A",0
24,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))/x,x)","d^{3} \left(\int \frac{a}{x}\, dx + \int 3 a c^{2} x\, dx + \int 3 a c^{4} x^{3}\, dx + \int a c^{6} x^{5}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 3 b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx + \int 3 b c^{4} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{6} x^{5} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a/x, x) + Integral(3*a*c**2*x, x) + Integral(3*a*c**4*x**3, x) + Integral(a*c**6*x**5, x) + Integral(b*asinh(c*x)/x, x) + Integral(3*b*c**2*x*asinh(c*x), x) + Integral(3*b*c**4*x**3*asinh(c*x), x) + Integral(b*c**6*x**5*asinh(c*x), x))","F",0
25,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))/x**2,x)","d^{3} \left(\int 3 a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int 3 a c^{4} x^{2}\, dx + \int a c^{6} x^{4}\, dx + \int 3 b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int 3 b c^{4} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{6} x^{4} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a*c**2, x) + Integral(a/x**2, x) + Integral(3*a*c**4*x**2, x) + Integral(a*c**6*x**4, x) + Integral(3*b*c**2*asinh(c*x), x) + Integral(b*asinh(c*x)/x**2, x) + Integral(3*b*c**4*x**2*asinh(c*x), x) + Integral(b*c**6*x**4*asinh(c*x), x))","F",0
26,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))/x**3,x)","d^{3} \left(\int \frac{a}{x^{3}}\, dx + \int \frac{3 a c^{2}}{x}\, dx + \int 3 a c^{4} x\, dx + \int a c^{6} x^{3}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 3 b c^{4} x \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{6} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a/x**3, x) + Integral(3*a*c**2/x, x) + Integral(3*a*c**4*x, x) + Integral(a*c**6*x**3, x) + Integral(b*asinh(c*x)/x**3, x) + Integral(3*b*c**2*asinh(c*x)/x, x) + Integral(3*b*c**4*x*asinh(c*x), x) + Integral(b*c**6*x**3*asinh(c*x), x))","F",0
27,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))/x**4,x)","d^{3} \left(\int 3 a c^{4}\, dx + \int \frac{a}{x^{4}}\, dx + \int \frac{3 a c^{2}}{x^{2}}\, dx + \int a c^{6} x^{2}\, dx + \int 3 b c^{4} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{3 b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int b c^{6} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a*c**4, x) + Integral(a/x**4, x) + Integral(3*a*c**2/x**2, x) + Integral(a*c**6*x**2, x) + Integral(3*b*c**4*asinh(c*x), x) + Integral(b*asinh(c*x)/x**4, x) + Integral(3*b*c**2*asinh(c*x)/x**2, x) + Integral(b*c**6*x**2*asinh(c*x), x))","F",0
28,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a x^{4}}{c^{2} x^{2} + 1}\, dx + \int \frac{b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a*x**4/(c**2*x**2 + 1), x) + Integral(b*x**4*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
29,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a x^{3}}{c^{2} x^{2} + 1}\, dx + \int \frac{b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a*x**3/(c**2*x**2 + 1), x) + Integral(b*x**3*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
30,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a x^{2}}{c^{2} x^{2} + 1}\, dx + \int \frac{b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a*x**2/(c**2*x**2 + 1), x) + Integral(b*x**2*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
31,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a x}{c^{2} x^{2} + 1}\, dx + \int \frac{b x \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a*x/(c**2*x**2 + 1), x) + Integral(b*x*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
32,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a}{c^{2} x^{2} + 1}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a/(c**2*x**2 + 1), x) + Integral(b*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
33,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d),x)","\frac{\int \frac{a}{c^{2} x^{3} + x}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{3} + x}\, dx}{d}"," ",0,"(Integral(a/(c**2*x**3 + x), x) + Integral(b*asinh(c*x)/(c**2*x**3 + x), x))/d","F",0
34,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a}{c^{2} x^{4} + x^{2}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{4} + x^{2}}\, dx}{d}"," ",0,"(Integral(a/(c**2*x**4 + x**2), x) + Integral(b*asinh(c*x)/(c**2*x**4 + x**2), x))/d","F",0
35,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d),x)","\frac{\int \frac{a}{c^{2} x^{5} + x^{3}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{5} + x^{3}}\, dx}{d}"," ",0,"(Integral(a/(c**2*x**5 + x**3), x) + Integral(b*asinh(c*x)/(c**2*x**5 + x**3), x))/d","F",0
36,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d),x)","\frac{\int \frac{a}{c^{2} x^{6} + x^{4}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{6} + x^{4}}\, dx}{d}"," ",0,"(Integral(a/(c**2*x**6 + x**4), x) + Integral(b*asinh(c*x)/(c**2*x**6 + x**4), x))/d","F",0
37,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a x^{4}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**4/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*x**4*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
38,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a x^{3}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**3/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*x**3*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
39,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a x^{2}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*x**2*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
40,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a x}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b x \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*x*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
41,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
42,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a}{c^{4} x^{5} + 2 c^{2} x^{3} + x}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{5} + 2 c^{2} x^{3} + x}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**4*x**5 + 2*c**2*x**3 + x), x) + Integral(b*asinh(c*x)/(c**4*x**5 + 2*c**2*x**3 + x), x))/d**2","F",0
43,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a}{c^{4} x^{6} + 2 c^{2} x^{4} + x^{2}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{6} + 2 c^{2} x^{4} + x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**4*x**6 + 2*c**2*x**4 + x**2), x) + Integral(b*asinh(c*x)/(c**4*x**6 + 2*c**2*x**4 + x**2), x))/d**2","F",0
44,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a}{c^{4} x^{7} + 2 c^{2} x^{5} + x^{3}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{7} + 2 c^{2} x^{5} + x^{3}}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**4*x**7 + 2*c**2*x**5 + x**3), x) + Integral(b*asinh(c*x)/(c**4*x**7 + 2*c**2*x**5 + x**3), x))/d**2","F",0
45,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a}{c^{4} x^{8} + 2 c^{2} x^{6} + x^{4}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{8} + 2 c^{2} x^{6} + x^{4}}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**4*x**8 + 2*c**2*x**6 + x**4), x) + Integral(b*asinh(c*x)/(c**4*x**8 + 2*c**2*x**6 + x**4), x))/d**2","F",0
46,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a x^{4}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**4/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b*x**4*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
47,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a x^{3}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**3/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b*x**3*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
48,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a x^{2}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b*x**2*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
49,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a x}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b x \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b*x*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
50,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
51,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a}{c^{6} x^{7} + 3 c^{4} x^{5} + 3 c^{2} x^{3} + x}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{7} + 3 c^{4} x^{5} + 3 c^{2} x^{3} + x}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**6*x**7 + 3*c**4*x**5 + 3*c**2*x**3 + x), x) + Integral(b*asinh(c*x)/(c**6*x**7 + 3*c**4*x**5 + 3*c**2*x**3 + x), x))/d**3","F",0
52,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a}{c^{6} x^{8} + 3 c^{4} x^{6} + 3 c^{2} x^{4} + x^{2}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{8} + 3 c^{4} x^{6} + 3 c^{2} x^{4} + x^{2}}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**6*x**8 + 3*c**4*x**6 + 3*c**2*x**4 + x**2), x) + Integral(b*asinh(c*x)/(c**6*x**8 + 3*c**4*x**6 + 3*c**2*x**4 + x**2), x))/d**3","F",0
53,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**6*x**9 + 3*c**4*x**7 + 3*c**2*x**5 + x**3), x) + Integral(b*asinh(c*x)/(c**6*x**9 + 3*c**4*x**7 + 3*c**2*x**5 + x**3), x))/d**3","F",0
54,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a}{c^{6} x^{10} + 3 c^{4} x^{8} + 3 c^{2} x^{6} + x^{4}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{10} + 3 c^{4} x^{8} + 3 c^{2} x^{6} + x^{4}}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**6*x**10 + 3*c**4*x**8 + 3*c**2*x**6 + x**4), x) + Integral(b*asinh(c*x)/(c**6*x**10 + 3*c**4*x**8 + 3*c**2*x**6 + x**4), x))/d**3","F",0
55,1,221,0,15.676913," ","integrate(x**3*(a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2),x)","\begin{cases} \frac{\sqrt{\pi} a x^{4} \sqrt{c^{2} x^{2} + 1}}{5} + \frac{\sqrt{\pi} a x^{2} \sqrt{c^{2} x^{2} + 1}}{15 c^{2}} - \frac{2 \sqrt{\pi} a \sqrt{c^{2} x^{2} + 1}}{15 c^{4}} - \frac{\sqrt{\pi} b c x^{5}}{25} + \frac{\sqrt{\pi} b x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{\sqrt{\pi} b x^{3}}{45 c} + \frac{\sqrt{\pi} b x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{15 c^{2}} + \frac{2 \sqrt{\pi} b x}{15 c^{3}} - \frac{2 \sqrt{\pi} b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{15 c^{4}} & \text{for}\: c \neq 0 \\\frac{\sqrt{\pi} a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(pi)*a*x**4*sqrt(c**2*x**2 + 1)/5 + sqrt(pi)*a*x**2*sqrt(c**2*x**2 + 1)/(15*c**2) - 2*sqrt(pi)*a*sqrt(c**2*x**2 + 1)/(15*c**4) - sqrt(pi)*b*c*x**5/25 + sqrt(pi)*b*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/5 - sqrt(pi)*b*x**3/(45*c) + sqrt(pi)*b*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(15*c**2) + 2*sqrt(pi)*b*x/(15*c**3) - 2*sqrt(pi)*b*sqrt(c**2*x**2 + 1)*asinh(c*x)/(15*c**4), Ne(c, 0)), (sqrt(pi)*a*x**4/4, True))","A",0
56,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2),x)","\sqrt{\pi} \left(\int a x^{2} \sqrt{c^{2} x^{2} + 1}\, dx + \int b x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a*x**2*sqrt(c**2*x**2 + 1), x) + Integral(b*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
57,1,141,0,2.203582," ","integrate(x*(a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2),x)","\begin{cases} \frac{\sqrt{\pi} a x^{2} \sqrt{c^{2} x^{2} + 1}}{3} + \frac{\sqrt{\pi} a \sqrt{c^{2} x^{2} + 1}}{3 c^{2}} - \frac{\sqrt{\pi} b c x^{3}}{9} + \frac{\sqrt{\pi} b x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{\sqrt{\pi} b x}{3 c} + \frac{\sqrt{\pi} b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c^{2}} & \text{for}\: c \neq 0 \\\frac{\sqrt{\pi} a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(pi)*a*x**2*sqrt(c**2*x**2 + 1)/3 + sqrt(pi)*a*sqrt(c**2*x**2 + 1)/(3*c**2) - sqrt(pi)*b*c*x**3/9 + sqrt(pi)*b*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/3 - sqrt(pi)*b*x/(3*c) + sqrt(pi)*b*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c**2), Ne(c, 0)), (sqrt(pi)*a*x**2/2, True))","A",0
58,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2),x)","\sqrt{\pi} \left(\int a \sqrt{c^{2} x^{2} + 1}\, dx + \int b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a*sqrt(c**2*x**2 + 1), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
59,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2)/x,x)","\sqrt{\pi} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a*sqrt(c**2*x**2 + 1)/x, x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x, x))","F",0
60,1,110,0,3.008172," ","integrate((a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2)/x**2,x)","- \frac{\sqrt{\pi} a c^{2} x}{\sqrt{c^{2} x^{2} + 1}} + \sqrt{\pi} a c \operatorname{asinh}{\left(c x \right)} - \frac{\sqrt{\pi} a}{x \sqrt{c^{2} x^{2} + 1}} + \sqrt{\pi} b c \log{\left(x \right)} + \frac{\sqrt{\pi} b c \operatorname{asinh}^{2}{\left(c x \right)}}{2} - \frac{\sqrt{\pi} b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}"," ",0,"-sqrt(pi)*a*c**2*x/sqrt(c**2*x**2 + 1) + sqrt(pi)*a*c*asinh(c*x) - sqrt(pi)*a/(x*sqrt(c**2*x**2 + 1)) + sqrt(pi)*b*c*log(x) + sqrt(pi)*b*c*asinh(c*x)**2/2 - sqrt(pi)*b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x","B",0
61,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2)/x**3,x)","\sqrt{\pi} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{3}}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a*sqrt(c**2*x**2 + 1)/x**3, x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**3, x))","F",0
62,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(pi*c**2*x**2+pi)**(1/2)/x**4,x)","\sqrt{\pi} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{4}}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a*sqrt(c**2*x**2 + 1)/x**4, x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**4, x))","F",0
63,-1,0,0,0.000000," ","integrate(x**3*(pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate(x**2*(pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,1,221,0,82.232218," ","integrate(x*(pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{\pi^{\frac{3}{2}} a c^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{5} + \frac{2 \pi^{\frac{3}{2}} a x^{2} \sqrt{c^{2} x^{2} + 1}}{5} + \frac{\pi^{\frac{3}{2}} a \sqrt{c^{2} x^{2} + 1}}{5 c^{2}} - \frac{\pi^{\frac{3}{2}} b c^{3} x^{5}}{25} + \frac{\pi^{\frac{3}{2}} b c^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{2 \pi^{\frac{3}{2}} b c x^{3}}{15} + \frac{2 \pi^{\frac{3}{2}} b x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{\pi^{\frac{3}{2}} b x}{5 c} + \frac{\pi^{\frac{3}{2}} b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{5 c^{2}} & \text{for}\: c \neq 0 \\\frac{\pi^{\frac{3}{2}} a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((pi**(3/2)*a*c**2*x**4*sqrt(c**2*x**2 + 1)/5 + 2*pi**(3/2)*a*x**2*sqrt(c**2*x**2 + 1)/5 + pi**(3/2)*a*sqrt(c**2*x**2 + 1)/(5*c**2) - pi**(3/2)*b*c**3*x**5/25 + pi**(3/2)*b*c**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/5 - 2*pi**(3/2)*b*c*x**3/15 + 2*pi**(3/2)*b*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/5 - pi**(3/2)*b*x/(5*c) + pi**(3/2)*b*sqrt(c**2*x**2 + 1)*asinh(c*x)/(5*c**2), Ne(c, 0)), (pi**(3/2)*a*x**2/2, True))","A",0
66,1,185,0,38.262993," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x)),x)","\begin{cases} \frac{\pi^{\frac{3}{2}} a c^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{4} + \frac{5 \pi^{\frac{3}{2}} a x \sqrt{c^{2} x^{2} + 1}}{8} + \frac{3 \pi^{\frac{3}{2}} a \operatorname{asinh}{\left(c x \right)}}{8 c} - \frac{\pi^{\frac{3}{2}} b c^{3} x^{4}}{16} + \frac{\pi^{\frac{3}{2}} b c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{5 \pi^{\frac{3}{2}} b c x^{2}}{16} + \frac{5 \pi^{\frac{3}{2}} b x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{8} + \frac{3 \pi^{\frac{3}{2}} b \operatorname{asinh}^{2}{\left(c x \right)}}{16 c} & \text{for}\: c \neq 0 \\\pi^{\frac{3}{2}} a x & \text{otherwise} \end{cases}"," ",0,"Piecewise((pi**(3/2)*a*c**2*x**3*sqrt(c**2*x**2 + 1)/4 + 5*pi**(3/2)*a*x*sqrt(c**2*x**2 + 1)/8 + 3*pi**(3/2)*a*asinh(c*x)/(8*c) - pi**(3/2)*b*c**3*x**4/16 + pi**(3/2)*b*c**2*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/4 - 5*pi**(3/2)*b*c*x**2/16 + 5*pi**(3/2)*b*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/8 + 3*pi**(3/2)*b*asinh(c*x)**2/(16*c), Ne(c, 0)), (pi**(3/2)*a*x, True))","A",0
67,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x))/x,x)","\pi^{\frac{3}{2}} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x}\, dx + \int a c^{2} x \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int b c^{2} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"pi**(3/2)*(Integral(a*sqrt(c**2*x**2 + 1)/x, x) + Integral(a*c**2*x*sqrt(c**2*x**2 + 1), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x, x) + Integral(b*c**2*x*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
68,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x))/x**2,x)","\pi^{\frac{3}{2}} \left(\int a c^{2} \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{2}}\, dx + \int b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"pi**(3/2)*(Integral(a*c**2*sqrt(c**2*x**2 + 1), x) + Integral(a*sqrt(c**2*x**2 + 1)/x**2, x) + Integral(b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**2, x))","F",0
69,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x))/x**3,x)","\pi^{\frac{3}{2}} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{3}}\, dx + \int \frac{a c^{2} \sqrt{c^{2} x^{2} + 1}}{x}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"pi**(3/2)*(Integral(a*sqrt(c**2*x**2 + 1)/x**3, x) + Integral(a*c**2*sqrt(c**2*x**2 + 1)/x, x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**3, x) + Integral(b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/x, x))","F",0
70,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x))/x**4,x)","\pi^{\frac{3}{2}} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{4}}\, dx + \int \frac{a c^{2} \sqrt{c^{2} x^{2} + 1}}{x^{2}}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"pi**(3/2)*(Integral(a*sqrt(c**2*x**2 + 1)/x**4, x) + Integral(a*c**2*sqrt(c**2*x**2 + 1)/x**2, x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**4, x) + Integral(b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**2, x))","F",0
71,-1,0,0,0.000000," ","integrate(x**3*(pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(x**2*(pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(x*(pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x))/x,x)","\pi^{\frac{5}{2}} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x}\, dx + \int 2 a c^{2} x \sqrt{c^{2} x^{2} + 1}\, dx + \int a c^{4} x^{3} \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 2 b c^{2} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{4} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"pi**(5/2)*(Integral(a*sqrt(c**2*x**2 + 1)/x, x) + Integral(2*a*c**2*x*sqrt(c**2*x**2 + 1), x) + Integral(a*c**4*x**3*sqrt(c**2*x**2 + 1), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x, x) + Integral(2*b*c**2*x*sqrt(c**2*x**2 + 1)*asinh(c*x), x) + Integral(b*c**4*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
76,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x))/x**2,x)","\pi^{\frac{5}{2}} \left(\int 2 a c^{2} \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{2}}\, dx + \int a c^{4} x^{2} \sqrt{c^{2} x^{2} + 1}\, dx + \int 2 b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int b c^{4} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"pi**(5/2)*(Integral(2*a*c**2*sqrt(c**2*x**2 + 1), x) + Integral(a*sqrt(c**2*x**2 + 1)/x**2, x) + Integral(a*c**4*x**2*sqrt(c**2*x**2 + 1), x) + Integral(2*b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**2, x) + Integral(b*c**4*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
77,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x))/x**3,x)","\pi^{\frac{5}{2}} \left(\int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{3}}\, dx + \int \frac{2 a c^{2} \sqrt{c^{2} x^{2} + 1}}{x}\, dx + \int a c^{4} x \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int b c^{4} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"pi**(5/2)*(Integral(a*sqrt(c**2*x**2 + 1)/x**3, x) + Integral(2*a*c**2*sqrt(c**2*x**2 + 1)/x, x) + Integral(a*c**4*x*sqrt(c**2*x**2 + 1), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**3, x) + Integral(2*b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/x, x) + Integral(b*c**4*x*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
78,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x))/x**4,x)","\pi^{\frac{5}{2}} \left(\int a c^{4} \sqrt{c^{2} x^{2} + 1}\, dx + \int \frac{a \sqrt{c^{2} x^{2} + 1}}{x^{4}}\, dx + \int \frac{2 a c^{2} \sqrt{c^{2} x^{2} + 1}}{x^{2}}\, dx + \int b c^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 b c^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"pi**(5/2)*(Integral(a*c**4*sqrt(c**2*x**2 + 1), x) + Integral(a*sqrt(c**2*x**2 + 1)/x**4, x) + Integral(2*a*c**2*sqrt(c**2*x**2 + 1)/x**2, x) + Integral(b*c**4*sqrt(c**2*x**2 + 1)*asinh(c*x), x) + Integral(b*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**4, x) + Integral(2*b*c**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/x**2, x))","F",0
79,0,0,0,0.000000," ","integrate(asinh(x)*(x**2+1)**(1/2),x)","\int \sqrt{x^{2} + 1} \operatorname{asinh}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(x**2 + 1)*asinh(x), x)","F",0
80,1,182,0,10.091187," ","integrate(x**5*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\frac{a \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} + 1}}{5 c^{2}} - \frac{4 x^{2} \sqrt{c^{2} x^{2} + 1}}{15 c^{4}} + \frac{8 \sqrt{c^{2} x^{2} + 1}}{15 c^{6}} & \text{for}\: c \neq 0 \\\frac{x^{6}}{6} & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}} + \frac{b \left(\begin{cases} - \frac{x^{5}}{25 c} + \frac{x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{5 c^{2}} + \frac{4 x^{3}}{45 c^{3}} - \frac{4 x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{15 c^{4}} - \frac{8 x}{15 c^{5}} + \frac{8 \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{15 c^{6}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}}"," ",0,"a*Piecewise((x**4*sqrt(c**2*x**2 + 1)/(5*c**2) - 4*x**2*sqrt(c**2*x**2 + 1)/(15*c**4) + 8*sqrt(c**2*x**2 + 1)/(15*c**6), Ne(c, 0)), (x**6/6, True))/sqrt(pi) + b*Piecewise((-x**5/(25*c) + x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(5*c**2) + 4*x**3/(45*c**3) - 4*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(15*c**4) - 8*x/(15*c**5) + 8*sqrt(c**2*x**2 + 1)*asinh(c*x)/(15*c**6), Ne(c, 0)), (0, True))/sqrt(pi)","A",0
81,1,185,0,9.015152," ","integrate(x**4*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\frac{a x^{5}}{4 \sqrt{\pi} \sqrt{c^{2} x^{2} + 1}} - \frac{a x^{3}}{8 \sqrt{\pi} c^{2} \sqrt{c^{2} x^{2} + 1}} - \frac{3 a x}{8 \sqrt{\pi} c^{4} \sqrt{c^{2} x^{2} + 1}} + \frac{3 a \operatorname{asinh}{\left(c x \right)}}{8 \sqrt{\pi} c^{5}} + \frac{b \left(\begin{cases} - \frac{x^{4}}{16 c} + \frac{x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4 c^{2}} + \frac{3 x^{2}}{16 c^{3}} - \frac{3 x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{8 c^{4}} + \frac{3 \operatorname{asinh}^{2}{\left(c x \right)}}{16 c^{5}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}}"," ",0,"a*x**5/(4*sqrt(pi)*sqrt(c**2*x**2 + 1)) - a*x**3/(8*sqrt(pi)*c**2*sqrt(c**2*x**2 + 1)) - 3*a*x/(8*sqrt(pi)*c**4*sqrt(c**2*x**2 + 1)) + 3*a*asinh(c*x)/(8*sqrt(pi)*c**5) + b*Piecewise((-x**4/(16*c) + x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(4*c**2) + 3*x**2/(16*c**3) - 3*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(8*c**4) + 3*asinh(c*x)**2/(16*c**5), Ne(c, 0)), (0, True))/sqrt(pi)","A",0
82,1,122,0,3.942800," ","integrate(x**3*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\frac{a \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} + 1}}{3 c^{2}} - \frac{2 \sqrt{c^{2} x^{2} + 1}}{3 c^{4}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}} + \frac{b \left(\begin{cases} - \frac{x^{3}}{9 c} + \frac{x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c^{2}} + \frac{2 x}{3 c^{3}} - \frac{2 \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c^{4}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}}"," ",0,"a*Piecewise((x**2*sqrt(c**2*x**2 + 1)/(3*c**2) - 2*sqrt(c**2*x**2 + 1)/(3*c**4), Ne(c, 0)), (x**4/4, True))/sqrt(pi) + b*Piecewise((-x**3/(9*c) + x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c**2) + 2*x/(3*c**3) - 2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c**4), Ne(c, 0)), (0, True))/sqrt(pi)","A",0
83,1,92,0,4.146944," ","integrate(x**2*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\frac{a x \sqrt{c^{2} x^{2} + 1}}{2 \sqrt{\pi} c^{2}} - \frac{a \operatorname{asinh}{\left(c x \right)}}{2 \sqrt{\pi} c^{3}} + \frac{b \left(\begin{cases} - \frac{x^{2}}{4 c} + \frac{x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2 c^{2}} - \frac{\operatorname{asinh}^{2}{\left(c x \right)}}{4 c^{3}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}}"," ",0,"a*x*sqrt(c**2*x**2 + 1)/(2*sqrt(pi)*c**2) - a*asinh(c*x)/(2*sqrt(pi)*c**3) + b*Piecewise((-x**2/(4*c) + x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(2*c**2) - asinh(c*x)**2/(4*c**3), Ne(c, 0)), (0, True))/sqrt(pi)","A",0
84,1,60,0,2.439211," ","integrate(x*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\frac{a \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: c^{2} = 0 \\\frac{\sqrt{c^{2} x^{2} + 1}}{c^{2}} & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}} + \frac{b \left(\begin{cases} - \frac{x}{c} + \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{c^{2}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\sqrt{\pi}}"," ",0,"a*Piecewise((x**2/2, Eq(c**2, 0)), (sqrt(c**2*x**2 + 1)/c**2, True))/sqrt(pi) + b*Piecewise((-x/c + sqrt(c**2*x**2 + 1)*asinh(c*x)/c**2, Ne(c, 0)), (0, True))/sqrt(pi)","A",0
85,1,85,0,2.523190," ","integrate((a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(1/2),x)","\begin{cases} a \left(\begin{cases} \frac{\sqrt{- \frac{1}{c^{2}}} \operatorname{asin}{\left(x \sqrt{- c^{2}} \right)}}{\sqrt{\pi}} & \text{for}\: \pi c^{2} < 0 \\\frac{\sqrt{\frac{1}{c^{2}}} \operatorname{asinh}{\left(x \sqrt{c^{2}} \right)}}{\sqrt{\pi}} & \text{for}\: \pi c^{2} > 0 \end{cases}\right) & \text{for}\: b = 0 \\\frac{a x}{\sqrt{\pi}} & \text{for}\: c = 0 \\\frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{2 \sqrt{\pi} b c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*Piecewise((sqrt(-1/c**2)*asin(x*sqrt(-c**2))/sqrt(pi), pi*c**2 < 0), (sqrt(c**(-2))*asinh(x*sqrt(c**2))/sqrt(pi), pi*c**2 > 0)), Eq(b, 0)), (a*x/sqrt(pi), Eq(c, 0)), ((a + b*asinh(c*x))**2/(2*sqrt(pi)*b*c), True))","A",0
86,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(pi*c**2*x**2+pi)**(1/2),x)","\frac{\int \frac{a}{x \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x \sqrt{c^{2} x^{2} + 1}}\, dx}{\sqrt{\pi}}"," ",0,"(Integral(a/(x*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(x*sqrt(c**2*x**2 + 1)), x))/sqrt(pi)","F",0
87,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(pi*c**2*x**2+pi)**(1/2),x)","\frac{\int \frac{a}{x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx}{\sqrt{\pi}}"," ",0,"(Integral(a/(x**2*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(x**2*sqrt(c**2*x**2 + 1)), x))/sqrt(pi)","F",0
88,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(pi*c**2*x**2+pi)**(1/2),x)","\frac{\int \frac{a}{x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx}{\sqrt{\pi}}"," ",0,"(Integral(a/(x**3*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(x**3*sqrt(c**2*x**2 + 1)), x))/sqrt(pi)","F",0
89,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(pi*c**2*x**2+pi)**(1/2),x)","\frac{\int \frac{a}{x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx}{\sqrt{\pi}}"," ",0,"(Integral(a/(x**4*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(x**4*sqrt(c**2*x**2 + 1)), x))/sqrt(pi)","F",0
90,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a x^{5}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{5} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a*x**5/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**5*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
91,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a x^{4}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a*x**4/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**4*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
92,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a x^{3}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a*x**3/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**3*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
93,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a x^{2}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a*x**2/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**2*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
94,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a x}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a*x/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
95,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
96,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a}{c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} + x \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} + x \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a/(c**2*x**3*sqrt(c**2*x**2 + 1) + x*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**2*x**3*sqrt(c**2*x**2 + 1) + x*sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
97,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a}{c^{2} x^{4} \sqrt{c^{2} x^{2} + 1} + x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{4} \sqrt{c^{2} x^{2} + 1} + x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a/(c**2*x**4*sqrt(c**2*x**2 + 1) + x**2*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**2*x**4*sqrt(c**2*x**2 + 1) + x**2*sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
98,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a}{c^{2} x^{5} \sqrt{c^{2} x^{2} + 1} + x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{5} \sqrt{c^{2} x^{2} + 1} + x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a/(c**2*x**5*sqrt(c**2*x**2 + 1) + x**3*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**2*x**5*sqrt(c**2*x**2 + 1) + x**3*sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
99,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a}{c^{2} x^{6} \sqrt{c^{2} x^{2} + 1} + x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{6} \sqrt{c^{2} x^{2} + 1} + x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a/(c**2*x**6*sqrt(c**2*x**2 + 1) + x**4*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**2*x**6*sqrt(c**2*x**2 + 1) + x**4*sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
100,0,0,0,0.000000," ","integrate(x**6*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x^{6}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{6} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x**6/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**6*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
101,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x^{5}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{5} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x**5/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**5*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
102,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x^{4}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x**4/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**4*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
103,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x^{3}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x**3/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**3*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
104,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x^{2}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x**2/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x**2*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
105,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a x}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b x \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a*x/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*x*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
106,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
107,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a}{c^{4} x^{5} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} + x \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{5} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} + x \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a/(c**4*x**5*sqrt(c**2*x**2 + 1) + 2*c**2*x**3*sqrt(c**2*x**2 + 1) + x*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**4*x**5*sqrt(c**2*x**2 + 1) + 2*c**2*x**3*sqrt(c**2*x**2 + 1) + x*sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
108,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a}{c^{4} x^{6} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{4} \sqrt{c^{2} x^{2} + 1} + x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{6} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{4} \sqrt{c^{2} x^{2} + 1} + x^{2} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a/(c**4*x**6*sqrt(c**2*x**2 + 1) + 2*c**2*x**4*sqrt(c**2*x**2 + 1) + x**2*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**4*x**6*sqrt(c**2*x**2 + 1) + 2*c**2*x**4*sqrt(c**2*x**2 + 1) + x**2*sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
109,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a}{c^{4} x^{7} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{5} \sqrt{c^{2} x^{2} + 1} + x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{7} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{5} \sqrt{c^{2} x^{2} + 1} + x^{3} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a/(c**4*x**7*sqrt(c**2*x**2 + 1) + 2*c**2*x**5*sqrt(c**2*x**2 + 1) + x**3*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**4*x**7*sqrt(c**2*x**2 + 1) + 2*c**2*x**5*sqrt(c**2*x**2 + 1) + x**3*sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
110,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a}{c^{4} x^{8} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{6} \sqrt{c^{2} x^{2} + 1} + x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{8} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{6} \sqrt{c^{2} x^{2} + 1} + x^{4} \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a/(c**4*x**8*sqrt(c**2*x**2 + 1) + 2*c**2*x**6*sqrt(c**2*x**2 + 1) + x**4*sqrt(c**2*x**2 + 1)), x) + Integral(b*asinh(c*x)/(c**4*x**8*sqrt(c**2*x**2 + 1) + 2*c**2*x**6*sqrt(c**2*x**2 + 1) + x**4*sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
111,0,0,0,0.000000," ","integrate(asinh(a*x)/(a**2*c*x**2+c)**(7/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(asinh(a*x)/(c*(a**2*x**2 + 1))**(7/2), x)","F",0
112,1,82,0,2.293770," ","integrate(x**4*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{4}}{16 a} + \frac{x^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{4 a^{2}} + \frac{3 x^{2}}{16 a^{3}} - \frac{3 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{8 a^{4}} + \frac{3 \operatorname{asinh}^{2}{\left(a x \right)}}{16 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**4/(16*a) + x**3*sqrt(a**2*x**2 + 1)*asinh(a*x)/(4*a**2) + 3*x**2/(16*a**3) - 3*x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(8*a**4) + 3*asinh(a*x)**2/(16*a**5), Ne(a, 0)), (0, True))","A",0
113,1,65,0,1.201506," ","integrate(x**3*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{3}}{9 a} + \frac{x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{3 a^{2}} + \frac{2 x}{3 a^{3}} - \frac{2 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{3 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**3/(9*a) + x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)/(3*a**2) + 2*x/(3*a**3) - 2*sqrt(a**2*x**2 + 1)*asinh(a*x)/(3*a**4), Ne(a, 0)), (0, True))","A",0
114,1,42,0,0.759808," ","integrate(x**2*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{2}}{4 a} + \frac{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{2 a^{2}} - \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{4 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**2/(4*a) + x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(2*a**2) - asinh(a*x)**2/(4*a**3), Ne(a, 0)), (0, True))","A",0
115,1,24,0,0.442744," ","integrate(x*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/a + sqrt(a**2*x**2 + 1)*asinh(a*x)/a**2, Ne(a, 0)), (0, True))","A",0
116,1,10,0,0.339619," ","integrate(asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{2 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a*x)**2/(2*a), Ne(a, 0)), (0, True))","A",0
117,0,0,0,0.000000," ","integrate(asinh(a*x)/x/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x*sqrt(a**2*x**2 + 1)), x)","F",0
118,0,0,0,0.000000," ","integrate(asinh(a*x)/x**2/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x**2*sqrt(a**2*x**2 + 1)), x)","F",0
119,0,0,0,0.000000," ","integrate(asinh(a*x)/x**3/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x**3*sqrt(a**2*x**2 + 1)), x)","F",0
120,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int x^{3} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x**3*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x)), x)","F",0
121,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int x^{2} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x**2*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x)), x)","F",0
122,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2),x)","\int x \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x)), x)","F",0
123,0,0,0,0.000000," ","integrate((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)\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x)), x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/x,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{x}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/x, x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/x**2,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{x^{2}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/x**2, x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/x**3,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{x^{3}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/x**3, x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(c**2*d*x**2+d)**(1/2)/x**4,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{x^{4}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))/x**4, x)","F",0
128,0,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x**3*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x)), x)","F",0
129,0,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x**2*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x)), x)","F",0
130,0,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\int x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x)), x)","F",0
131,0,0,0,0.000000," ","integrate((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)\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x)), x)","F",0
132,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))/x,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)}{x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))/x, x)","F",0
133,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))/x**2,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)}{x^{2}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))/x**2, x)","F",0
134,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))/x**3,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)}{x^{3}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))/x**3, x)","F",0
135,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))/x**4,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)}{x^{4}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))/x**4, x)","F",0
136,-1,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\int \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x)), x)","F",0
140,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))/x,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)}{x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))/x, x)","F",0
141,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))/x**2,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)}{x^{2}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))/x**2, x)","F",0
142,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))/x**3,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)}{x^{3}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))/x**3, x)","F",0
143,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))/x**4,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)}{x^{4}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))/x**4, x)","F",0
144,0,0,0,0.000000," ","integrate(asinh(x)*(x**2+1)**(1/2),x)","\int \sqrt{x^{2} + 1} \operatorname{asinh}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(x**2 + 1)*asinh(x), x)","F",0
145,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
146,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
147,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
148,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
150,0,0,0,0.000000," ","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
151,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x*sqrt(d*(c**2*x**2 + 1))), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{2} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**2*sqrt(d*(c**2*x**2 + 1))), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{3} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**3*sqrt(d*(c**2*x**2 + 1))), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{4} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**4*sqrt(d*(c**2*x**2 + 1))), x)","F",0
155,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
159,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
160,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
161,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
162,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**2*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
163,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**3*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
164,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{4} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**4*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
165,0,0,0,0.000000," ","integrate(x**6*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{6} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**6*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
168,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
172,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x/(c**2*d*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**2*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**3/(c**2*d*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(x**3*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
175,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))/x**4/(c**2*d*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,0,0,0,0.000000," ","integrate(asinh(a*x)/(a**2*c*x**2+c)**(7/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(asinh(a*x)/(c*(a**2*x**2 + 1))**(7/2), x)","F",0
177,1,82,0,2.266954," ","integrate(x**4*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{4}}{16 a} + \frac{x^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{4 a^{2}} + \frac{3 x^{2}}{16 a^{3}} - \frac{3 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{8 a^{4}} + \frac{3 \operatorname{asinh}^{2}{\left(a x \right)}}{16 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**4/(16*a) + x**3*sqrt(a**2*x**2 + 1)*asinh(a*x)/(4*a**2) + 3*x**2/(16*a**3) - 3*x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(8*a**4) + 3*asinh(a*x)**2/(16*a**5), Ne(a, 0)), (0, True))","A",0
178,1,65,0,1.203238," ","integrate(x**3*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{3}}{9 a} + \frac{x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{3 a^{2}} + \frac{2 x}{3 a^{3}} - \frac{2 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{3 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**3/(9*a) + x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)/(3*a**2) + 2*x/(3*a**3) - 2*sqrt(a**2*x**2 + 1)*asinh(a*x)/(3*a**4), Ne(a, 0)), (0, True))","A",0
179,1,42,0,0.753513," ","integrate(x**2*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{2}}{4 a} + \frac{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{2 a^{2}} - \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{4 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**2/(4*a) + x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(2*a**2) - asinh(a*x)**2/(4*a**3), Ne(a, 0)), (0, True))","A",0
180,1,24,0,0.429180," ","integrate(x*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/a + sqrt(a**2*x**2 + 1)*asinh(a*x)/a**2, Ne(a, 0)), (0, True))","A",0
181,1,10,0,0.339417," ","integrate(asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{2 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a*x)**2/(2*a), Ne(a, 0)), (0, True))","A",0
182,0,0,0,0.000000," ","integrate(asinh(a*x)/x/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x*sqrt(a**2*x**2 + 1)), x)","F",0
183,0,0,0,0.000000," ","integrate(asinh(a*x)/x**2/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x**2*sqrt(a**2*x**2 + 1)), x)","F",0
184,0,0,0,0.000000," ","integrate(asinh(a*x)/x**3/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}{\left(a x \right)}}{x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)/(x**3*sqrt(a**2*x**2 + 1)), x)","F",0
185,0,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**3*(a+b*asinh(c*x)),x)","d^{3} \left(\int a x^{m}\, dx + \int b x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int 3 a c^{2} x^{2} x^{m}\, dx + \int 3 a c^{4} x^{4} x^{m}\, dx + \int a c^{6} x^{6} x^{m}\, dx + \int 3 b c^{2} x^{2} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int 3 b c^{4} x^{4} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{6} x^{6} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a*x**m, x) + Integral(b*x**m*asinh(c*x), x) + Integral(3*a*c**2*x**2*x**m, x) + Integral(3*a*c**4*x**4*x**m, x) + Integral(a*c**6*x**6*x**m, x) + Integral(3*b*c**2*x**2*x**m*asinh(c*x), x) + Integral(3*b*c**4*x**4*x**m*asinh(c*x), x) + Integral(b*c**6*x**6*x**m*asinh(c*x), x))","F",0
186,0,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**2*(a+b*asinh(c*x)),x)","d^{2} \left(\int a x^{m}\, dx + \int b x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int 2 a c^{2} x^{2} x^{m}\, dx + \int a c^{4} x^{4} x^{m}\, dx + \int 2 b c^{2} x^{2} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int b c^{4} x^{4} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a*x**m, x) + Integral(b*x**m*asinh(c*x), x) + Integral(2*a*c**2*x**2*x**m, x) + Integral(a*c**4*x**4*x**m, x) + Integral(2*b*c**2*x**2*x**m*asinh(c*x), x) + Integral(b*c**4*x**4*x**m*asinh(c*x), x))","F",0
187,0,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)*(a+b*asinh(c*x)),x)","d \left(\int a x^{m}\, dx + \int b x^{m} \operatorname{asinh}{\left(c x \right)}\, dx + \int a c^{2} x^{2} x^{m}\, dx + \int b c^{2} x^{2} x^{m} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a*x**m, x) + Integral(b*x**m*asinh(c*x), x) + Integral(a*c**2*x**2*x**m, x) + Integral(b*c**2*x**2*x**m*asinh(c*x), x))","F",0
188,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d),x)","\frac{\int \frac{a x^{m}}{c^{2} x^{2} + 1}\, dx + \int \frac{b x^{m} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a*x**m/(c**2*x**2 + 1), x) + Integral(b*x**m*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
189,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a x^{m}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b x^{m} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**m/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b*x**m*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
190,-1,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,0,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(1/2)*(a+b*asinh(c*x)),x)","\int x^{m} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(x**m*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x)), x)","F",0
194,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{m} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*(a + b*asinh(c*x))/sqrt(d*(c**2*x**2 + 1)), x)","F",0
195,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{m} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*(a + b*asinh(c*x))/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
196,-1,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))/(c**2*d*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,0,0,0,0.000000," ","integrate(x**m*asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{m} \operatorname{asinh}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m*asinh(a*x)/sqrt(a**2*x**2 + 1), x)","F",0
198,1,388,0,11.399742," ","integrate(x**4*(c**2*d*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{2} d x^{7}}{7} + \frac{a^{2} d x^{5}}{5} + \frac{2 a b c^{2} d x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{2 a b c d x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{2 a b d x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{38 a b d x^{4} \sqrt{c^{2} x^{2} + 1}}{1225 c} + \frac{152 a b d x^{2} \sqrt{c^{2} x^{2} + 1}}{3675 c^{3}} - \frac{304 a b d \sqrt{c^{2} x^{2} + 1}}{3675 c^{5}} + \frac{b^{2} c^{2} d x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{2 b^{2} c^{2} d x^{7}}{343} - \frac{2 b^{2} c d x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{49} + \frac{b^{2} d x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{38 b^{2} d x^{5}}{6125} - \frac{38 b^{2} d x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{1225 c} - \frac{152 b^{2} d x^{3}}{11025 c^{2}} + \frac{152 b^{2} d x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3675 c^{3}} + \frac{304 b^{2} d x}{3675 c^{4}} - \frac{304 b^{2} d \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3675 c^{5}} & \text{for}\: c \neq 0 \\\frac{a^{2} d x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*d*x**7/7 + a**2*d*x**5/5 + 2*a*b*c**2*d*x**7*asinh(c*x)/7 - 2*a*b*c*d*x**6*sqrt(c**2*x**2 + 1)/49 + 2*a*b*d*x**5*asinh(c*x)/5 - 38*a*b*d*x**4*sqrt(c**2*x**2 + 1)/(1225*c) + 152*a*b*d*x**2*sqrt(c**2*x**2 + 1)/(3675*c**3) - 304*a*b*d*sqrt(c**2*x**2 + 1)/(3675*c**5) + b**2*c**2*d*x**7*asinh(c*x)**2/7 + 2*b**2*c**2*d*x**7/343 - 2*b**2*c*d*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/49 + b**2*d*x**5*asinh(c*x)**2/5 + 38*b**2*d*x**5/6125 - 38*b**2*d*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(1225*c) - 152*b**2*d*x**3/(11025*c**2) + 152*b**2*d*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3675*c**3) + 304*b**2*d*x/(3675*c**4) - 304*b**2*d*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3675*c**5), Ne(c, 0)), (a**2*d*x**5/5, True))","A",0
199,1,332,0,7.857592," ","integrate(x**3*(c**2*d*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{2} d x^{6}}{6} + \frac{a^{2} d x^{4}}{4} + \frac{a b c^{2} d x^{6} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{a b c d x^{5} \sqrt{c^{2} x^{2} + 1}}{18} + \frac{a b d x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{a b d x^{3} \sqrt{c^{2} x^{2} + 1}}{18 c} + \frac{a b d x \sqrt{c^{2} x^{2} + 1}}{12 c^{3}} - \frac{a b d \operatorname{asinh}{\left(c x \right)}}{12 c^{4}} + \frac{b^{2} c^{2} d x^{6} \operatorname{asinh}^{2}{\left(c x \right)}}{6} + \frac{b^{2} c^{2} d x^{6}}{108} - \frac{b^{2} c d x^{5} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{18} + \frac{b^{2} d x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{b^{2} d x^{4}}{72} - \frac{b^{2} d x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{18 c} - \frac{b^{2} d x^{2}}{24 c^{2}} + \frac{b^{2} d x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{12 c^{3}} - \frac{b^{2} d \operatorname{asinh}^{2}{\left(c x \right)}}{24 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} d x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*d*x**6/6 + a**2*d*x**4/4 + a*b*c**2*d*x**6*asinh(c*x)/3 - a*b*c*d*x**5*sqrt(c**2*x**2 + 1)/18 + a*b*d*x**4*asinh(c*x)/2 - a*b*d*x**3*sqrt(c**2*x**2 + 1)/(18*c) + a*b*d*x*sqrt(c**2*x**2 + 1)/(12*c**3) - a*b*d*asinh(c*x)/(12*c**4) + b**2*c**2*d*x**6*asinh(c*x)**2/6 + b**2*c**2*d*x**6/108 - b**2*c*d*x**5*sqrt(c**2*x**2 + 1)*asinh(c*x)/18 + b**2*d*x**4*asinh(c*x)**2/4 + b**2*d*x**4/72 - b**2*d*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(18*c) - b**2*d*x**2/(24*c**2) + b**2*d*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(12*c**3) - b**2*d*asinh(c*x)**2/(24*c**4), Ne(c, 0)), (a**2*d*x**4/4, True))","A",0
200,1,313,0,5.211941," ","integrate(x**2*(c**2*d*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{2} d x^{5}}{5} + \frac{a^{2} d x^{3}}{3} + \frac{2 a b c^{2} d x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{2 a b c d x^{4} \sqrt{c^{2} x^{2} + 1}}{25} + \frac{2 a b d x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{26 a b d x^{2} \sqrt{c^{2} x^{2} + 1}}{225 c} + \frac{52 a b d \sqrt{c^{2} x^{2} + 1}}{225 c^{3}} + \frac{b^{2} c^{2} d x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{2 b^{2} c^{2} d x^{5}}{125} - \frac{2 b^{2} c d x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25} + \frac{b^{2} d x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{26 b^{2} d x^{3}}{675} - \frac{26 b^{2} d x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{225 c} - \frac{52 b^{2} d x}{225 c^{2}} + \frac{52 b^{2} d \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{225 c^{3}} & \text{for}\: c \neq 0 \\\frac{a^{2} d x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*d*x**5/5 + a**2*d*x**3/3 + 2*a*b*c**2*d*x**5*asinh(c*x)/5 - 2*a*b*c*d*x**4*sqrt(c**2*x**2 + 1)/25 + 2*a*b*d*x**3*asinh(c*x)/3 - 26*a*b*d*x**2*sqrt(c**2*x**2 + 1)/(225*c) + 52*a*b*d*sqrt(c**2*x**2 + 1)/(225*c**3) + b**2*c**2*d*x**5*asinh(c*x)**2/5 + 2*b**2*c**2*d*x**5/125 - 2*b**2*c*d*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/25 + b**2*d*x**3*asinh(c*x)**2/3 + 26*b**2*d*x**3/675 - 26*b**2*d*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(225*c) - 52*b**2*d*x/(225*c**2) + 52*b**2*d*sqrt(c**2*x**2 + 1)*asinh(c*x)/(225*c**3), Ne(c, 0)), (a**2*d*x**3/3, True))","A",0
201,1,269,0,3.332485," ","integrate(x*(c**2*d*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{2} d x^{4}}{4} + \frac{a^{2} d x^{2}}{2} + \frac{a b c^{2} d x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{a b c d x^{3} \sqrt{c^{2} x^{2} + 1}}{8} + a b d x^{2} \operatorname{asinh}{\left(c x \right)} - \frac{5 a b d x \sqrt{c^{2} x^{2} + 1}}{16 c} + \frac{5 a b d \operatorname{asinh}{\left(c x \right)}}{16 c^{2}} + \frac{b^{2} c^{2} d x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{b^{2} c^{2} d x^{4}}{32} - \frac{b^{2} c d x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{8} + \frac{b^{2} d x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{5 b^{2} d x^{2}}{32} - \frac{5 b^{2} d x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{16 c} + \frac{5 b^{2} d \operatorname{asinh}^{2}{\left(c x \right)}}{32 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*d*x**4/4 + a**2*d*x**2/2 + a*b*c**2*d*x**4*asinh(c*x)/2 - a*b*c*d*x**3*sqrt(c**2*x**2 + 1)/8 + a*b*d*x**2*asinh(c*x) - 5*a*b*d*x*sqrt(c**2*x**2 + 1)/(16*c) + 5*a*b*d*asinh(c*x)/(16*c**2) + b**2*c**2*d*x**4*asinh(c*x)**2/4 + b**2*c**2*d*x**4/32 - b**2*c*d*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/8 + b**2*d*x**2*asinh(c*x)**2/2 + 5*b**2*d*x**2/32 - 5*b**2*d*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(16*c) + 5*b**2*d*asinh(c*x)**2/(32*c**2), Ne(c, 0)), (a**2*d*x**2/2, True))","A",0
202,1,224,0,1.453130," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{2} d x^{3}}{3} + a^{2} d x + \frac{2 a b c^{2} d x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{2 a b c d x^{2} \sqrt{c^{2} x^{2} + 1}}{9} + 2 a b d x \operatorname{asinh}{\left(c x \right)} - \frac{14 a b d \sqrt{c^{2} x^{2} + 1}}{9 c} + \frac{b^{2} c^{2} d x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{2 b^{2} c^{2} d x^{3}}{27} - \frac{2 b^{2} c d x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9} + b^{2} d x \operatorname{asinh}^{2}{\left(c x \right)} + \frac{14 b^{2} d x}{9} - \frac{14 b^{2} d \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c} & \text{for}\: c \neq 0 \\a^{2} d x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*d*x**3/3 + a**2*d*x + 2*a*b*c**2*d*x**3*asinh(c*x)/3 - 2*a*b*c*d*x**2*sqrt(c**2*x**2 + 1)/9 + 2*a*b*d*x*asinh(c*x) - 14*a*b*d*sqrt(c**2*x**2 + 1)/(9*c) + b**2*c**2*d*x**3*asinh(c*x)**2/3 + 2*b**2*c**2*d*x**3/27 - 2*b**2*c*d*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/9 + b**2*d*x*asinh(c*x)**2 + 14*b**2*d*x/9 - 14*b**2*d*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c), Ne(c, 0)), (a**2*d*x, True))","A",0
203,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))**2/x,x)","d \left(\int \frac{a^{2}}{x}\, dx + \int a^{2} c^{2} x\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int b^{2} c^{2} x \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 2 a b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a**2/x, x) + Integral(a**2*c**2*x, x) + Integral(b**2*asinh(c*x)**2/x, x) + Integral(2*a*b*asinh(c*x)/x, x) + Integral(b**2*c**2*x*asinh(c*x)**2, x) + Integral(2*a*b*c**2*x*asinh(c*x), x))","F",0
204,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))**2/x**2,x)","d \left(\int a^{2} c^{2}\, dx + \int \frac{a^{2}}{x^{2}}\, dx + \int b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int 2 a b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d*(Integral(a**2*c**2, x) + Integral(a**2/x**2, x) + Integral(b**2*c**2*asinh(c*x)**2, x) + Integral(b**2*asinh(c*x)**2/x**2, x) + Integral(2*a*b*c**2*asinh(c*x), x) + Integral(2*a*b*asinh(c*x)/x**2, x))","F",0
205,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))**2/x**3,x)","d \left(\int \frac{a^{2}}{x^{3}}\, dx + \int \frac{a^{2} c^{2}}{x}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{2 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a**2/x**3, x) + Integral(a**2*c**2/x, x) + Integral(b**2*asinh(c*x)**2/x**3, x) + Integral(2*a*b*asinh(c*x)/x**3, x) + Integral(b**2*c**2*asinh(c*x)**2/x, x) + Integral(2*a*b*c**2*asinh(c*x)/x, x))","F",0
206,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)*(a+b*asinh(c*x))**2/x**4,x)","d \left(\int \frac{a^{2}}{x^{4}}\, dx + \int \frac{a^{2} c^{2}}{x^{2}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d*(Integral(a**2/x**4, x) + Integral(a**2*c**2/x**2, x) + Integral(b**2*asinh(c*x)**2/x**4, x) + Integral(2*a*b*asinh(c*x)/x**4, x) + Integral(b**2*c**2*asinh(c*x)**2/x**2, x) + Integral(2*a*b*c**2*asinh(c*x)/x**2, x))","F",0
207,1,563,0,30.818649," ","integrate(x**4*(c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{4} d^{2} x^{9}}{9} + \frac{2 a^{2} c^{2} d^{2} x^{7}}{7} + \frac{a^{2} d^{2} x^{5}}{5} + \frac{2 a b c^{4} d^{2} x^{9} \operatorname{asinh}{\left(c x \right)}}{9} - \frac{2 a b c^{3} d^{2} x^{8} \sqrt{c^{2} x^{2} + 1}}{81} + \frac{4 a b c^{2} d^{2} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{212 a b c d^{2} x^{6} \sqrt{c^{2} x^{2} + 1}}{3969} + \frac{2 a b d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{526 a b d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{33075 c} + \frac{2104 a b d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c^{3}} - \frac{4208 a b d^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c^{5}} + \frac{b^{2} c^{4} d^{2} x^{9} \operatorname{asinh}^{2}{\left(c x \right)}}{9} + \frac{2 b^{2} c^{4} d^{2} x^{9}}{729} - \frac{2 b^{2} c^{3} d^{2} x^{8} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{81} + \frac{2 b^{2} c^{2} d^{2} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{212 b^{2} c^{2} d^{2} x^{7}}{27783} - \frac{212 b^{2} c d^{2} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3969} + \frac{b^{2} d^{2} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{526 b^{2} d^{2} x^{5}}{165375} - \frac{526 b^{2} d^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{33075 c} - \frac{2104 b^{2} d^{2} x^{3}}{297675 c^{2}} + \frac{2104 b^{2} d^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{99225 c^{3}} + \frac{4208 b^{2} d^{2} x}{99225 c^{4}} - \frac{4208 b^{2} d^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{99225 c^{5}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{2} x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*d**2*x**9/9 + 2*a**2*c**2*d**2*x**7/7 + a**2*d**2*x**5/5 + 2*a*b*c**4*d**2*x**9*asinh(c*x)/9 - 2*a*b*c**3*d**2*x**8*sqrt(c**2*x**2 + 1)/81 + 4*a*b*c**2*d**2*x**7*asinh(c*x)/7 - 212*a*b*c*d**2*x**6*sqrt(c**2*x**2 + 1)/3969 + 2*a*b*d**2*x**5*asinh(c*x)/5 - 526*a*b*d**2*x**4*sqrt(c**2*x**2 + 1)/(33075*c) + 2104*a*b*d**2*x**2*sqrt(c**2*x**2 + 1)/(99225*c**3) - 4208*a*b*d**2*sqrt(c**2*x**2 + 1)/(99225*c**5) + b**2*c**4*d**2*x**9*asinh(c*x)**2/9 + 2*b**2*c**4*d**2*x**9/729 - 2*b**2*c**3*d**2*x**8*sqrt(c**2*x**2 + 1)*asinh(c*x)/81 + 2*b**2*c**2*d**2*x**7*asinh(c*x)**2/7 + 212*b**2*c**2*d**2*x**7/27783 - 212*b**2*c*d**2*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/3969 + b**2*d**2*x**5*asinh(c*x)**2/5 + 526*b**2*d**2*x**5/165375 - 526*b**2*d**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(33075*c) - 2104*b**2*d**2*x**3/(297675*c**2) + 2104*b**2*d**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(99225*c**3) + 4208*b**2*d**2*x/(99225*c**4) - 4208*b**2*d**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(99225*c**5), Ne(c, 0)), (a**2*d**2*x**5/5, True))","A",0
208,1,515,0,22.948524," ","integrate(x**3*(c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{4} d^{2} x^{8}}{8} + \frac{a^{2} c^{2} d^{2} x^{6}}{3} + \frac{a^{2} d^{2} x^{4}}{4} + \frac{a b c^{4} d^{2} x^{8} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{a b c^{3} d^{2} x^{7} \sqrt{c^{2} x^{2} + 1}}{32} + \frac{2 a b c^{2} d^{2} x^{6} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{43 a b c d^{2} x^{5} \sqrt{c^{2} x^{2} + 1}}{576} + \frac{a b d^{2} x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{73 a b d^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{2304 c} + \frac{73 a b d^{2} x \sqrt{c^{2} x^{2} + 1}}{1536 c^{3}} - \frac{73 a b d^{2} \operatorname{asinh}{\left(c x \right)}}{1536 c^{4}} + \frac{b^{2} c^{4} d^{2} x^{8} \operatorname{asinh}^{2}{\left(c x \right)}}{8} + \frac{b^{2} c^{4} d^{2} x^{8}}{256} - \frac{b^{2} c^{3} d^{2} x^{7} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{32} + \frac{b^{2} c^{2} d^{2} x^{6} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{43 b^{2} c^{2} d^{2} x^{6}}{3456} - \frac{43 b^{2} c d^{2} x^{5} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{576} + \frac{b^{2} d^{2} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{73 b^{2} d^{2} x^{4}}{9216} - \frac{73 b^{2} d^{2} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2304 c} - \frac{73 b^{2} d^{2} x^{2}}{3072 c^{2}} + \frac{73 b^{2} d^{2} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{1536 c^{3}} - \frac{73 b^{2} d^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{3072 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*d**2*x**8/8 + a**2*c**2*d**2*x**6/3 + a**2*d**2*x**4/4 + a*b*c**4*d**2*x**8*asinh(c*x)/4 - a*b*c**3*d**2*x**7*sqrt(c**2*x**2 + 1)/32 + 2*a*b*c**2*d**2*x**6*asinh(c*x)/3 - 43*a*b*c*d**2*x**5*sqrt(c**2*x**2 + 1)/576 + a*b*d**2*x**4*asinh(c*x)/2 - 73*a*b*d**2*x**3*sqrt(c**2*x**2 + 1)/(2304*c) + 73*a*b*d**2*x*sqrt(c**2*x**2 + 1)/(1536*c**3) - 73*a*b*d**2*asinh(c*x)/(1536*c**4) + b**2*c**4*d**2*x**8*asinh(c*x)**2/8 + b**2*c**4*d**2*x**8/256 - b**2*c**3*d**2*x**7*sqrt(c**2*x**2 + 1)*asinh(c*x)/32 + b**2*c**2*d**2*x**6*asinh(c*x)**2/3 + 43*b**2*c**2*d**2*x**6/3456 - 43*b**2*c*d**2*x**5*sqrt(c**2*x**2 + 1)*asinh(c*x)/576 + b**2*d**2*x**4*asinh(c*x)**2/4 + 73*b**2*d**2*x**4/9216 - 73*b**2*d**2*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(2304*c) - 73*b**2*d**2*x**2/(3072*c**2) + 73*b**2*d**2*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(1536*c**3) - 73*b**2*d**2*asinh(c*x)**2/(3072*c**4), Ne(c, 0)), (a**2*d**2*x**4/4, True))","A",0
209,1,483,0,12.701952," ","integrate(x**2*(c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{4} d^{2} x^{7}}{7} + \frac{2 a^{2} c^{2} d^{2} x^{5}}{5} + \frac{a^{2} d^{2} x^{3}}{3} + \frac{2 a b c^{4} d^{2} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{2 a b c^{3} d^{2} x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{4 a b c^{2} d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{136 a b c d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{1225} + \frac{2 a b d^{2} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{818 a b d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{11025 c} + \frac{1636 a b d^{2} \sqrt{c^{2} x^{2} + 1}}{11025 c^{3}} + \frac{b^{2} c^{4} d^{2} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{2 b^{2} c^{4} d^{2} x^{7}}{343} - \frac{2 b^{2} c^{3} d^{2} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{49} + \frac{2 b^{2} c^{2} d^{2} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{136 b^{2} c^{2} d^{2} x^{5}}{6125} - \frac{136 b^{2} c d^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{1225} + \frac{b^{2} d^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{818 b^{2} d^{2} x^{3}}{33075} - \frac{818 b^{2} d^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{11025 c} - \frac{1636 b^{2} d^{2} x}{11025 c^{2}} + \frac{1636 b^{2} d^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{11025 c^{3}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{2} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*d**2*x**7/7 + 2*a**2*c**2*d**2*x**5/5 + a**2*d**2*x**3/3 + 2*a*b*c**4*d**2*x**7*asinh(c*x)/7 - 2*a*b*c**3*d**2*x**6*sqrt(c**2*x**2 + 1)/49 + 4*a*b*c**2*d**2*x**5*asinh(c*x)/5 - 136*a*b*c*d**2*x**4*sqrt(c**2*x**2 + 1)/1225 + 2*a*b*d**2*x**3*asinh(c*x)/3 - 818*a*b*d**2*x**2*sqrt(c**2*x**2 + 1)/(11025*c) + 1636*a*b*d**2*sqrt(c**2*x**2 + 1)/(11025*c**3) + b**2*c**4*d**2*x**7*asinh(c*x)**2/7 + 2*b**2*c**4*d**2*x**7/343 - 2*b**2*c**3*d**2*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/49 + 2*b**2*c**2*d**2*x**5*asinh(c*x)**2/5 + 136*b**2*c**2*d**2*x**5/6125 - 136*b**2*c*d**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/1225 + b**2*d**2*x**3*asinh(c*x)**2/3 + 818*b**2*d**2*x**3/33075 - 818*b**2*d**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(11025*c) - 1636*b**2*d**2*x/(11025*c**2) + 1636*b**2*d**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(11025*c**3), Ne(c, 0)), (a**2*d**2*x**3/3, True))","A",0
210,1,430,0,8.816278," ","integrate(x*(c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{4} d^{2} x^{6}}{6} + \frac{a^{2} c^{2} d^{2} x^{4}}{2} + \frac{a^{2} d^{2} x^{2}}{2} + \frac{a b c^{4} d^{2} x^{6} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{a b c^{3} d^{2} x^{5} \sqrt{c^{2} x^{2} + 1}}{18} + a b c^{2} d^{2} x^{4} \operatorname{asinh}{\left(c x \right)} - \frac{13 a b c d^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{72} + a b d^{2} x^{2} \operatorname{asinh}{\left(c x \right)} - \frac{11 a b d^{2} x \sqrt{c^{2} x^{2} + 1}}{48 c} + \frac{11 a b d^{2} \operatorname{asinh}{\left(c x \right)}}{48 c^{2}} + \frac{b^{2} c^{4} d^{2} x^{6} \operatorname{asinh}^{2}{\left(c x \right)}}{6} + \frac{b^{2} c^{4} d^{2} x^{6}}{108} - \frac{b^{2} c^{3} d^{2} x^{5} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{18} + \frac{b^{2} c^{2} d^{2} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{13 b^{2} c^{2} d^{2} x^{4}}{288} - \frac{13 b^{2} c d^{2} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{72} + \frac{b^{2} d^{2} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{11 b^{2} d^{2} x^{2}}{96} - \frac{11 b^{2} d^{2} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{48 c} + \frac{11 b^{2} d^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{96 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{2} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*d**2*x**6/6 + a**2*c**2*d**2*x**4/2 + a**2*d**2*x**2/2 + a*b*c**4*d**2*x**6*asinh(c*x)/3 - a*b*c**3*d**2*x**5*sqrt(c**2*x**2 + 1)/18 + a*b*c**2*d**2*x**4*asinh(c*x) - 13*a*b*c*d**2*x**3*sqrt(c**2*x**2 + 1)/72 + a*b*d**2*x**2*asinh(c*x) - 11*a*b*d**2*x*sqrt(c**2*x**2 + 1)/(48*c) + 11*a*b*d**2*asinh(c*x)/(48*c**2) + b**2*c**4*d**2*x**6*asinh(c*x)**2/6 + b**2*c**4*d**2*x**6/108 - b**2*c**3*d**2*x**5*sqrt(c**2*x**2 + 1)*asinh(c*x)/18 + b**2*c**2*d**2*x**4*asinh(c*x)**2/2 + 13*b**2*c**2*d**2*x**4/288 - 13*b**2*c*d**2*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/72 + b**2*d**2*x**2*asinh(c*x)**2/2 + 11*b**2*d**2*x**2/96 - 11*b**2*d**2*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(48*c) + 11*b**2*d**2*asinh(c*x)**2/(96*c**2), Ne(c, 0)), (a**2*d**2*x**2/2, True))","A",0
211,1,389,0,4.765993," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{4} d^{2} x^{5}}{5} + \frac{2 a^{2} c^{2} d^{2} x^{3}}{3} + a^{2} d^{2} x + \frac{2 a b c^{4} d^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{2 a b c^{3} d^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25} + \frac{4 a b c^{2} d^{2} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{76 a b c d^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{225} + 2 a b d^{2} x \operatorname{asinh}{\left(c x \right)} - \frac{298 a b d^{2} \sqrt{c^{2} x^{2} + 1}}{225 c} + \frac{b^{2} c^{4} d^{2} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{2 b^{2} c^{4} d^{2} x^{5}}{125} - \frac{2 b^{2} c^{3} d^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25} + \frac{2 b^{2} c^{2} d^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{76 b^{2} c^{2} d^{2} x^{3}}{675} - \frac{76 b^{2} c d^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{225} + b^{2} d^{2} x \operatorname{asinh}^{2}{\left(c x \right)} + \frac{298 b^{2} d^{2} x}{225} - \frac{298 b^{2} d^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{225 c} & \text{for}\: c \neq 0 \\a^{2} d^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*d**2*x**5/5 + 2*a**2*c**2*d**2*x**3/3 + a**2*d**2*x + 2*a*b*c**4*d**2*x**5*asinh(c*x)/5 - 2*a*b*c**3*d**2*x**4*sqrt(c**2*x**2 + 1)/25 + 4*a*b*c**2*d**2*x**3*asinh(c*x)/3 - 76*a*b*c*d**2*x**2*sqrt(c**2*x**2 + 1)/225 + 2*a*b*d**2*x*asinh(c*x) - 298*a*b*d**2*sqrt(c**2*x**2 + 1)/(225*c) + b**2*c**4*d**2*x**5*asinh(c*x)**2/5 + 2*b**2*c**4*d**2*x**5/125 - 2*b**2*c**3*d**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/25 + 2*b**2*c**2*d**2*x**3*asinh(c*x)**2/3 + 76*b**2*c**2*d**2*x**3/675 - 76*b**2*c*d**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/225 + b**2*d**2*x*asinh(c*x)**2 + 298*b**2*d**2*x/225 - 298*b**2*d**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(225*c), Ne(c, 0)), (a**2*d**2*x, True))","A",0
212,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2/x,x)","d^{2} \left(\int \frac{a^{2}}{x}\, dx + \int 2 a^{2} c^{2} x\, dx + \int a^{2} c^{4} x^{3}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 2 b^{2} c^{2} x \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{4} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 4 a b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx + \int 2 a b c^{4} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2/x, x) + Integral(2*a**2*c**2*x, x) + Integral(a**2*c**4*x**3, x) + Integral(b**2*asinh(c*x)**2/x, x) + Integral(2*a*b*asinh(c*x)/x, x) + Integral(2*b**2*c**2*x*asinh(c*x)**2, x) + Integral(b**2*c**4*x**3*asinh(c*x)**2, x) + Integral(4*a*b*c**2*x*asinh(c*x), x) + Integral(2*a*b*c**4*x**3*asinh(c*x), x))","F",0
213,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2/x**2,x)","d^{2} \left(\int 2 a^{2} c^{2}\, dx + \int \frac{a^{2}}{x^{2}}\, dx + \int a^{2} c^{4} x^{2}\, dx + \int 2 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int 4 a b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int b^{2} c^{4} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 2 a b c^{4} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(2*a**2*c**2, x) + Integral(a**2/x**2, x) + Integral(a**2*c**4*x**2, x) + Integral(2*b**2*c**2*asinh(c*x)**2, x) + Integral(b**2*asinh(c*x)**2/x**2, x) + Integral(4*a*b*c**2*asinh(c*x), x) + Integral(2*a*b*asinh(c*x)/x**2, x) + Integral(b**2*c**4*x**2*asinh(c*x)**2, x) + Integral(2*a*b*c**4*x**2*asinh(c*x), x))","F",0
214,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2/x**3,x)","d^{2} \left(\int \frac{a^{2}}{x^{3}}\, dx + \int \frac{2 a^{2} c^{2}}{x}\, dx + \int a^{2} c^{4} x\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int b^{2} c^{4} x \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{4 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 2 a b c^{4} x \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2/x**3, x) + Integral(2*a**2*c**2/x, x) + Integral(a**2*c**4*x, x) + Integral(b**2*asinh(c*x)**2/x**3, x) + Integral(2*a*b*asinh(c*x)/x**3, x) + Integral(2*b**2*c**2*asinh(c*x)**2/x, x) + Integral(b**2*c**4*x*asinh(c*x)**2, x) + Integral(4*a*b*c**2*asinh(c*x)/x, x) + Integral(2*a*b*c**4*x*asinh(c*x), x))","F",0
215,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2*(a+b*asinh(c*x))**2/x**4,x)","d^{2} \left(\int a^{2} c^{4}\, dx + \int \frac{a^{2}}{x^{4}}\, dx + \int \frac{2 a^{2} c^{2}}{x^{2}}\, dx + \int b^{2} c^{4} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int 2 a b c^{4} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{4 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d**2*(Integral(a**2*c**4, x) + Integral(a**2/x**4, x) + Integral(2*a**2*c**2/x**2, x) + Integral(b**2*c**4*asinh(c*x)**2, x) + Integral(b**2*asinh(c*x)**2/x**4, x) + Integral(2*a*b*c**4*asinh(c*x), x) + Integral(2*a*b*asinh(c*x)/x**4, x) + Integral(2*b**2*c**2*asinh(c*x)**2/x**2, x) + Integral(4*a*b*c**2*asinh(c*x)/x**2, x))","F",0
216,1,702,0,71.194585," ","integrate(x**4*(c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{6} d^{3} x^{11}}{11} + \frac{a^{2} c^{4} d^{3} x^{9}}{3} + \frac{3 a^{2} c^{2} d^{3} x^{7}}{7} + \frac{a^{2} d^{3} x^{5}}{5} + \frac{2 a b c^{6} d^{3} x^{11} \operatorname{asinh}{\left(c x \right)}}{11} - \frac{2 a b c^{5} d^{3} x^{10} \sqrt{c^{2} x^{2} + 1}}{121} + \frac{2 a b c^{4} d^{3} x^{9} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{182 a b c^{3} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1}}{3267} + \frac{6 a b c^{2} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{9410 a b c d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{160083} + \frac{2 a b d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{12622 a b d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{1334025 c} + \frac{50488 a b d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{4002075 c^{3}} - \frac{100976 a b d^{3} \sqrt{c^{2} x^{2} + 1}}{4002075 c^{5}} + \frac{b^{2} c^{6} d^{3} x^{11} \operatorname{asinh}^{2}{\left(c x \right)}}{11} + \frac{2 b^{2} c^{6} d^{3} x^{11}}{1331} - \frac{2 b^{2} c^{5} d^{3} x^{10} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{121} + \frac{b^{2} c^{4} d^{3} x^{9} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{182 b^{2} c^{4} d^{3} x^{9}}{29403} - \frac{182 b^{2} c^{3} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3267} + \frac{3 b^{2} c^{2} d^{3} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{9410 b^{2} c^{2} d^{3} x^{7}}{1120581} - \frac{9410 b^{2} c d^{3} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{160083} + \frac{b^{2} d^{3} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{12622 b^{2} d^{3} x^{5}}{6670125} - \frac{12622 b^{2} d^{3} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{1334025 c} - \frac{50488 b^{2} d^{3} x^{3}}{12006225 c^{2}} + \frac{50488 b^{2} d^{3} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4002075 c^{3}} + \frac{100976 b^{2} d^{3} x}{4002075 c^{4}} - \frac{100976 b^{2} d^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4002075 c^{5}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{3} x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**6*d**3*x**11/11 + a**2*c**4*d**3*x**9/3 + 3*a**2*c**2*d**3*x**7/7 + a**2*d**3*x**5/5 + 2*a*b*c**6*d**3*x**11*asinh(c*x)/11 - 2*a*b*c**5*d**3*x**10*sqrt(c**2*x**2 + 1)/121 + 2*a*b*c**4*d**3*x**9*asinh(c*x)/3 - 182*a*b*c**3*d**3*x**8*sqrt(c**2*x**2 + 1)/3267 + 6*a*b*c**2*d**3*x**7*asinh(c*x)/7 - 9410*a*b*c*d**3*x**6*sqrt(c**2*x**2 + 1)/160083 + 2*a*b*d**3*x**5*asinh(c*x)/5 - 12622*a*b*d**3*x**4*sqrt(c**2*x**2 + 1)/(1334025*c) + 50488*a*b*d**3*x**2*sqrt(c**2*x**2 + 1)/(4002075*c**3) - 100976*a*b*d**3*sqrt(c**2*x**2 + 1)/(4002075*c**5) + b**2*c**6*d**3*x**11*asinh(c*x)**2/11 + 2*b**2*c**6*d**3*x**11/1331 - 2*b**2*c**5*d**3*x**10*sqrt(c**2*x**2 + 1)*asinh(c*x)/121 + b**2*c**4*d**3*x**9*asinh(c*x)**2/3 + 182*b**2*c**4*d**3*x**9/29403 - 182*b**2*c**3*d**3*x**8*sqrt(c**2*x**2 + 1)*asinh(c*x)/3267 + 3*b**2*c**2*d**3*x**7*asinh(c*x)**2/7 + 9410*b**2*c**2*d**3*x**7/1120581 - 9410*b**2*c*d**3*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/160083 + b**2*d**3*x**5*asinh(c*x)**2/5 + 12622*b**2*d**3*x**5/6670125 - 12622*b**2*d**3*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(1334025*c) - 50488*b**2*d**3*x**3/(12006225*c**2) + 50488*b**2*d**3*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(4002075*c**3) + 100976*b**2*d**3*x/(4002075*c**4) - 100976*b**2*d**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(4002075*c**5), Ne(c, 0)), (a**2*d**3*x**5/5, True))","A",0
217,1,654,0,55.916314," ","integrate(x**3*(c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{6} d^{3} x^{10}}{10} + \frac{3 a^{2} c^{4} d^{3} x^{8}}{8} + \frac{a^{2} c^{2} d^{3} x^{6}}{2} + \frac{a^{2} d^{3} x^{4}}{4} + \frac{a b c^{6} d^{3} x^{10} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{a b c^{5} d^{3} x^{9} \sqrt{c^{2} x^{2} + 1}}{50} + \frac{3 a b c^{4} d^{3} x^{8} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{57 a b c^{3} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1}}{800} + a b c^{2} d^{3} x^{6} \operatorname{asinh}{\left(c x \right)} - \frac{401 a b c d^{3} x^{5} \sqrt{c^{2} x^{2} + 1}}{4800} + \frac{a b d^{3} x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{79 a b d^{3} x^{3} \sqrt{c^{2} x^{2} + 1}}{3840 c} + \frac{79 a b d^{3} x \sqrt{c^{2} x^{2} + 1}}{2560 c^{3}} - \frac{79 a b d^{3} \operatorname{asinh}{\left(c x \right)}}{2560 c^{4}} + \frac{b^{2} c^{6} d^{3} x^{10} \operatorname{asinh}^{2}{\left(c x \right)}}{10} + \frac{b^{2} c^{6} d^{3} x^{10}}{500} - \frac{b^{2} c^{5} d^{3} x^{9} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{50} + \frac{3 b^{2} c^{4} d^{3} x^{8} \operatorname{asinh}^{2}{\left(c x \right)}}{8} + \frac{57 b^{2} c^{4} d^{3} x^{8}}{6400} - \frac{57 b^{2} c^{3} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{800} + \frac{b^{2} c^{2} d^{3} x^{6} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{401 b^{2} c^{2} d^{3} x^{6}}{28800} - \frac{401 b^{2} c d^{3} x^{5} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4800} + \frac{b^{2} d^{3} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{79 b^{2} d^{3} x^{4}}{15360} - \frac{79 b^{2} d^{3} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3840 c} - \frac{79 b^{2} d^{3} x^{2}}{5120 c^{2}} + \frac{79 b^{2} d^{3} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2560 c^{3}} - \frac{79 b^{2} d^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{5120 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{3} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**6*d**3*x**10/10 + 3*a**2*c**4*d**3*x**8/8 + a**2*c**2*d**3*x**6/2 + a**2*d**3*x**4/4 + a*b*c**6*d**3*x**10*asinh(c*x)/5 - a*b*c**5*d**3*x**9*sqrt(c**2*x**2 + 1)/50 + 3*a*b*c**4*d**3*x**8*asinh(c*x)/4 - 57*a*b*c**3*d**3*x**7*sqrt(c**2*x**2 + 1)/800 + a*b*c**2*d**3*x**6*asinh(c*x) - 401*a*b*c*d**3*x**5*sqrt(c**2*x**2 + 1)/4800 + a*b*d**3*x**4*asinh(c*x)/2 - 79*a*b*d**3*x**3*sqrt(c**2*x**2 + 1)/(3840*c) + 79*a*b*d**3*x*sqrt(c**2*x**2 + 1)/(2560*c**3) - 79*a*b*d**3*asinh(c*x)/(2560*c**4) + b**2*c**6*d**3*x**10*asinh(c*x)**2/10 + b**2*c**6*d**3*x**10/500 - b**2*c**5*d**3*x**9*sqrt(c**2*x**2 + 1)*asinh(c*x)/50 + 3*b**2*c**4*d**3*x**8*asinh(c*x)**2/8 + 57*b**2*c**4*d**3*x**8/6400 - 57*b**2*c**3*d**3*x**7*sqrt(c**2*x**2 + 1)*asinh(c*x)/800 + b**2*c**2*d**3*x**6*asinh(c*x)**2/2 + 401*b**2*c**2*d**3*x**6/28800 - 401*b**2*c*d**3*x**5*sqrt(c**2*x**2 + 1)*asinh(c*x)/4800 + b**2*d**3*x**4*asinh(c*x)**2/4 + 79*b**2*d**3*x**4/15360 - 79*b**2*d**3*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3840*c) - 79*b**2*d**3*x**2/(5120*c**2) + 79*b**2*d**3*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(2560*c**3) - 79*b**2*d**3*asinh(c*x)**2/(5120*c**4), Ne(c, 0)), (a**2*d**3*x**4/4, True))","A",0
218,1,626,0,32.872639," ","integrate(x**2*(c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{6} d^{3} x^{9}}{9} + \frac{3 a^{2} c^{4} d^{3} x^{7}}{7} + \frac{3 a^{2} c^{2} d^{3} x^{5}}{5} + \frac{a^{2} d^{3} x^{3}}{3} + \frac{2 a b c^{6} d^{3} x^{9} \operatorname{asinh}{\left(c x \right)}}{9} - \frac{2 a b c^{5} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1}}{81} + \frac{6 a b c^{4} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{374 a b c^{3} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{3969} + \frac{6 a b c^{2} d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{4198 a b c d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{33075} + \frac{2 a b d^{3} x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{5258 a b d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{99225 c} + \frac{10516 a b d^{3} \sqrt{c^{2} x^{2} + 1}}{99225 c^{3}} + \frac{b^{2} c^{6} d^{3} x^{9} \operatorname{asinh}^{2}{\left(c x \right)}}{9} + \frac{2 b^{2} c^{6} d^{3} x^{9}}{729} - \frac{2 b^{2} c^{5} d^{3} x^{8} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{81} + \frac{3 b^{2} c^{4} d^{3} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{374 b^{2} c^{4} d^{3} x^{7}}{27783} - \frac{374 b^{2} c^{3} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3969} + \frac{3 b^{2} c^{2} d^{3} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{4198 b^{2} c^{2} d^{3} x^{5}}{165375} - \frac{4198 b^{2} c d^{3} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{33075} + \frac{b^{2} d^{3} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{5258 b^{2} d^{3} x^{3}}{297675} - \frac{5258 b^{2} d^{3} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{99225 c} - \frac{10516 b^{2} d^{3} x}{99225 c^{2}} + \frac{10516 b^{2} d^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{99225 c^{3}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{3} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**6*d**3*x**9/9 + 3*a**2*c**4*d**3*x**7/7 + 3*a**2*c**2*d**3*x**5/5 + a**2*d**3*x**3/3 + 2*a*b*c**6*d**3*x**9*asinh(c*x)/9 - 2*a*b*c**5*d**3*x**8*sqrt(c**2*x**2 + 1)/81 + 6*a*b*c**4*d**3*x**7*asinh(c*x)/7 - 374*a*b*c**3*d**3*x**6*sqrt(c**2*x**2 + 1)/3969 + 6*a*b*c**2*d**3*x**5*asinh(c*x)/5 - 4198*a*b*c*d**3*x**4*sqrt(c**2*x**2 + 1)/33075 + 2*a*b*d**3*x**3*asinh(c*x)/3 - 5258*a*b*d**3*x**2*sqrt(c**2*x**2 + 1)/(99225*c) + 10516*a*b*d**3*sqrt(c**2*x**2 + 1)/(99225*c**3) + b**2*c**6*d**3*x**9*asinh(c*x)**2/9 + 2*b**2*c**6*d**3*x**9/729 - 2*b**2*c**5*d**3*x**8*sqrt(c**2*x**2 + 1)*asinh(c*x)/81 + 3*b**2*c**4*d**3*x**7*asinh(c*x)**2/7 + 374*b**2*c**4*d**3*x**7/27783 - 374*b**2*c**3*d**3*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/3969 + 3*b**2*c**2*d**3*x**5*asinh(c*x)**2/5 + 4198*b**2*c**2*d**3*x**5/165375 - 4198*b**2*c*d**3*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/33075 + b**2*d**3*x**3*asinh(c*x)**2/3 + 5258*b**2*d**3*x**3/297675 - 5258*b**2*d**3*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(99225*c) - 10516*b**2*d**3*x/(99225*c**2) + 10516*b**2*d**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(99225*c**3), Ne(c, 0)), (a**2*d**3*x**3/3, True))","A",0
219,1,573,0,24.280849," ","integrate(x*(c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{6} d^{3} x^{8}}{8} + \frac{a^{2} c^{4} d^{3} x^{6}}{2} + \frac{3 a^{2} c^{2} d^{3} x^{4}}{4} + \frac{a^{2} d^{3} x^{2}}{2} + \frac{a b c^{6} d^{3} x^{8} \operatorname{asinh}{\left(c x \right)}}{4} - \frac{a b c^{5} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1}}{32} + a b c^{4} d^{3} x^{6} \operatorname{asinh}{\left(c x \right)} - \frac{25 a b c^{3} d^{3} x^{5} \sqrt{c^{2} x^{2} + 1}}{192} + \frac{3 a b c^{2} d^{3} x^{4} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{163 a b c d^{3} x^{3} \sqrt{c^{2} x^{2} + 1}}{768} + a b d^{3} x^{2} \operatorname{asinh}{\left(c x \right)} - \frac{93 a b d^{3} x \sqrt{c^{2} x^{2} + 1}}{512 c} + \frac{93 a b d^{3} \operatorname{asinh}{\left(c x \right)}}{512 c^{2}} + \frac{b^{2} c^{6} d^{3} x^{8} \operatorname{asinh}^{2}{\left(c x \right)}}{8} + \frac{b^{2} c^{6} d^{3} x^{8}}{256} - \frac{b^{2} c^{5} d^{3} x^{7} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{32} + \frac{b^{2} c^{4} d^{3} x^{6} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{25 b^{2} c^{4} d^{3} x^{6}}{1152} - \frac{25 b^{2} c^{3} d^{3} x^{5} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{192} + \frac{3 b^{2} c^{2} d^{3} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{163 b^{2} c^{2} d^{3} x^{4}}{3072} - \frac{163 b^{2} c d^{3} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{768} + \frac{b^{2} d^{3} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{2} + \frac{93 b^{2} d^{3} x^{2}}{1024} - \frac{93 b^{2} d^{3} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{512 c} + \frac{93 b^{2} d^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{1024 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{3} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**6*d**3*x**8/8 + a**2*c**4*d**3*x**6/2 + 3*a**2*c**2*d**3*x**4/4 + a**2*d**3*x**2/2 + a*b*c**6*d**3*x**8*asinh(c*x)/4 - a*b*c**5*d**3*x**7*sqrt(c**2*x**2 + 1)/32 + a*b*c**4*d**3*x**6*asinh(c*x) - 25*a*b*c**3*d**3*x**5*sqrt(c**2*x**2 + 1)/192 + 3*a*b*c**2*d**3*x**4*asinh(c*x)/2 - 163*a*b*c*d**3*x**3*sqrt(c**2*x**2 + 1)/768 + a*b*d**3*x**2*asinh(c*x) - 93*a*b*d**3*x*sqrt(c**2*x**2 + 1)/(512*c) + 93*a*b*d**3*asinh(c*x)/(512*c**2) + b**2*c**6*d**3*x**8*asinh(c*x)**2/8 + b**2*c**6*d**3*x**8/256 - b**2*c**5*d**3*x**7*sqrt(c**2*x**2 + 1)*asinh(c*x)/32 + b**2*c**4*d**3*x**6*asinh(c*x)**2/2 + 25*b**2*c**4*d**3*x**6/1152 - 25*b**2*c**3*d**3*x**5*sqrt(c**2*x**2 + 1)*asinh(c*x)/192 + 3*b**2*c**2*d**3*x**4*asinh(c*x)**2/4 + 163*b**2*c**2*d**3*x**4/3072 - 163*b**2*c*d**3*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/768 + b**2*d**3*x**2*asinh(c*x)**2/2 + 93*b**2*d**3*x**2/1024 - 93*b**2*d**3*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/(512*c) + 93*b**2*d**3*asinh(c*x)**2/(1024*c**2), Ne(c, 0)), (a**2*d**3*x**2/2, True))","A",0
220,1,524,0,13.357174," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{a^{2} c^{6} d^{3} x^{7}}{7} + \frac{3 a^{2} c^{4} d^{3} x^{5}}{5} + a^{2} c^{2} d^{3} x^{3} + a^{2} d^{3} x + \frac{2 a b c^{6} d^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{2 a b c^{5} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{49} + \frac{6 a b c^{4} d^{3} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{234 a b c^{3} d^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{1225} + 2 a b c^{2} d^{3} x^{3} \operatorname{asinh}{\left(c x \right)} - \frac{1514 a b c d^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{3675} + 2 a b d^{3} x \operatorname{asinh}{\left(c x \right)} - \frac{4322 a b d^{3} \sqrt{c^{2} x^{2} + 1}}{3675 c} + \frac{b^{2} c^{6} d^{3} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{2 b^{2} c^{6} d^{3} x^{7}}{343} - \frac{2 b^{2} c^{5} d^{3} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{49} + \frac{3 b^{2} c^{4} d^{3} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{234 b^{2} c^{4} d^{3} x^{5}}{6125} - \frac{234 b^{2} c^{3} d^{3} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{1225} + b^{2} c^{2} d^{3} x^{3} \operatorname{asinh}^{2}{\left(c x \right)} + \frac{1514 b^{2} c^{2} d^{3} x^{3}}{11025} - \frac{1514 b^{2} c d^{3} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3675} + b^{2} d^{3} x \operatorname{asinh}^{2}{\left(c x \right)} + \frac{4322 b^{2} d^{3} x}{3675} - \frac{4322 b^{2} d^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3675 c} & \text{for}\: c \neq 0 \\a^{2} d^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**6*d**3*x**7/7 + 3*a**2*c**4*d**3*x**5/5 + a**2*c**2*d**3*x**3 + a**2*d**3*x + 2*a*b*c**6*d**3*x**7*asinh(c*x)/7 - 2*a*b*c**5*d**3*x**6*sqrt(c**2*x**2 + 1)/49 + 6*a*b*c**4*d**3*x**5*asinh(c*x)/5 - 234*a*b*c**3*d**3*x**4*sqrt(c**2*x**2 + 1)/1225 + 2*a*b*c**2*d**3*x**3*asinh(c*x) - 1514*a*b*c*d**3*x**2*sqrt(c**2*x**2 + 1)/3675 + 2*a*b*d**3*x*asinh(c*x) - 4322*a*b*d**3*sqrt(c**2*x**2 + 1)/(3675*c) + b**2*c**6*d**3*x**7*asinh(c*x)**2/7 + 2*b**2*c**6*d**3*x**7/343 - 2*b**2*c**5*d**3*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/49 + 3*b**2*c**4*d**3*x**5*asinh(c*x)**2/5 + 234*b**2*c**4*d**3*x**5/6125 - 234*b**2*c**3*d**3*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/1225 + b**2*c**2*d**3*x**3*asinh(c*x)**2 + 1514*b**2*c**2*d**3*x**3/11025 - 1514*b**2*c*d**3*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/3675 + b**2*d**3*x*asinh(c*x)**2 + 4322*b**2*d**3*x/3675 - 4322*b**2*d**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3675*c), Ne(c, 0)), (a**2*d**3*x, True))","A",0
221,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2/x,x)","d^{3} \left(\int \frac{a^{2}}{x}\, dx + \int 3 a^{2} c^{2} x\, dx + \int 3 a^{2} c^{4} x^{3}\, dx + \int a^{2} c^{6} x^{5}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 3 b^{2} c^{2} x \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 3 b^{2} c^{4} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{6} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 6 a b c^{2} x \operatorname{asinh}{\left(c x \right)}\, dx + \int 6 a b c^{4} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx + \int 2 a b c^{6} x^{5} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2/x, x) + Integral(3*a**2*c**2*x, x) + Integral(3*a**2*c**4*x**3, x) + Integral(a**2*c**6*x**5, x) + Integral(b**2*asinh(c*x)**2/x, x) + Integral(2*a*b*asinh(c*x)/x, x) + Integral(3*b**2*c**2*x*asinh(c*x)**2, x) + Integral(3*b**2*c**4*x**3*asinh(c*x)**2, x) + Integral(b**2*c**6*x**5*asinh(c*x)**2, x) + Integral(6*a*b*c**2*x*asinh(c*x), x) + Integral(6*a*b*c**4*x**3*asinh(c*x), x) + Integral(2*a*b*c**6*x**5*asinh(c*x), x))","F",0
222,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2/x**2,x)","d^{3} \left(\int 3 a^{2} c^{2}\, dx + \int \frac{a^{2}}{x^{2}}\, dx + \int 3 a^{2} c^{4} x^{2}\, dx + \int a^{2} c^{6} x^{4}\, dx + \int 3 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int 6 a b c^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int 3 b^{2} c^{4} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{6} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 6 a b c^{4} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx + \int 2 a b c^{6} x^{4} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a**2*c**2, x) + Integral(a**2/x**2, x) + Integral(3*a**2*c**4*x**2, x) + Integral(a**2*c**6*x**4, x) + Integral(3*b**2*c**2*asinh(c*x)**2, x) + Integral(b**2*asinh(c*x)**2/x**2, x) + Integral(6*a*b*c**2*asinh(c*x), x) + Integral(2*a*b*asinh(c*x)/x**2, x) + Integral(3*b**2*c**4*x**2*asinh(c*x)**2, x) + Integral(b**2*c**6*x**4*asinh(c*x)**2, x) + Integral(6*a*b*c**4*x**2*asinh(c*x), x) + Integral(2*a*b*c**6*x**4*asinh(c*x), x))","F",0
223,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2/x**3,x)","d^{3} \left(\int \frac{a^{2}}{x^{3}}\, dx + \int \frac{3 a^{2} c^{2}}{x}\, dx + \int 3 a^{2} c^{4} x\, dx + \int a^{2} c^{6} x^{3}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x}\, dx + \int 3 b^{2} c^{4} x \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{6} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{6 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x}\, dx + \int 6 a b c^{4} x \operatorname{asinh}{\left(c x \right)}\, dx + \int 2 a b c^{6} x^{3} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2/x**3, x) + Integral(3*a**2*c**2/x, x) + Integral(3*a**2*c**4*x, x) + Integral(a**2*c**6*x**3, x) + Integral(b**2*asinh(c*x)**2/x**3, x) + Integral(2*a*b*asinh(c*x)/x**3, x) + Integral(3*b**2*c**2*asinh(c*x)**2/x, x) + Integral(3*b**2*c**4*x*asinh(c*x)**2, x) + Integral(b**2*c**6*x**3*asinh(c*x)**2, x) + Integral(6*a*b*c**2*asinh(c*x)/x, x) + Integral(6*a*b*c**4*x*asinh(c*x), x) + Integral(2*a*b*c**6*x**3*asinh(c*x), x))","F",0
224,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**3*(a+b*asinh(c*x))**2/x**4,x)","d^{3} \left(\int 3 a^{2} c^{4}\, dx + \int \frac{a^{2}}{x^{4}}\, dx + \int \frac{3 a^{2} c^{2}}{x^{2}}\, dx + \int a^{2} c^{6} x^{2}\, dx + \int 3 b^{2} c^{4} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int 6 a b c^{4} \operatorname{asinh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int b^{2} c^{6} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int \frac{6 a b c^{2} \operatorname{asinh}{\left(c x \right)}}{x^{2}}\, dx + \int 2 a b c^{6} x^{2} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a**2*c**4, x) + Integral(a**2/x**4, x) + Integral(3*a**2*c**2/x**2, x) + Integral(a**2*c**6*x**2, x) + Integral(3*b**2*c**4*asinh(c*x)**2, x) + Integral(b**2*asinh(c*x)**2/x**4, x) + Integral(6*a*b*c**4*asinh(c*x), x) + Integral(2*a*b*asinh(c*x)/x**4, x) + Integral(3*b**2*c**2*asinh(c*x)**2/x**2, x) + Integral(b**2*c**6*x**2*asinh(c*x)**2, x) + Integral(6*a*b*c**2*asinh(c*x)/x**2, x) + Integral(2*a*b*c**6*x**2*asinh(c*x), x))","F",0
225,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2} x^{4}}{c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a**2*x**4/(c**2*x**2 + 1), x) + Integral(b**2*x**4*asinh(c*x)**2/(c**2*x**2 + 1), x) + Integral(2*a*b*x**4*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
226,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2} x^{3}}{c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a**2*x**3/(c**2*x**2 + 1), x) + Integral(b**2*x**3*asinh(c*x)**2/(c**2*x**2 + 1), x) + Integral(2*a*b*x**3*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
227,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2} x^{2}}{c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a**2*x**2/(c**2*x**2 + 1), x) + Integral(b**2*x**2*asinh(c*x)**2/(c**2*x**2 + 1), x) + Integral(2*a*b*x**2*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
228,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2} x}{c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a**2*x/(c**2*x**2 + 1), x) + Integral(b**2*x*asinh(c*x)**2/(c**2*x**2 + 1), x) + Integral(2*a*b*x*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
229,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2}}{c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} + 1}\, dx}{d}"," ",0,"(Integral(a**2/(c**2*x**2 + 1), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**2 + 1), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**2 + 1), x))/d","F",0
230,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2}}{c^{2} x^{3} + x}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{3} + x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{3} + x}\, dx}{d}"," ",0,"(Integral(a**2/(c**2*x**3 + x), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**3 + x), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**3 + x), x))/d","F",0
231,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2}}{c^{2} x^{4} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{4} + x^{2}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{4} + x^{2}}\, dx}{d}"," ",0,"(Integral(a**2/(c**2*x**4 + x**2), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**4 + x**2), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**4 + x**2), x))/d","F",0
232,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2}}{c^{2} x^{5} + x^{3}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{5} + x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{5} + x^{3}}\, dx}{d}"," ",0,"(Integral(a**2/(c**2*x**5 + x**3), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**5 + x**3), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**5 + x**3), x))/d","F",0
233,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d),x)","\frac{\int \frac{a^{2}}{c^{2} x^{6} + x^{4}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{6} + x^{4}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{6} + x^{4}}\, dx}{d}"," ",0,"(Integral(a**2/(c**2*x**6 + x**4), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**6 + x**4), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**6 + x**4), x))/d","F",0
234,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2} x^{4}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**4/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b**2*x**4*asinh(c*x)**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(2*a*b*x**4*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
235,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2} x^{3}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**3/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b**2*x**3*asinh(c*x)**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(2*a*b*x**3*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
236,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2} x^{2}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b**2*x**2*asinh(c*x)**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(2*a*b*x**2*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
237,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2} x}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b**2*x*asinh(c*x)**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(2*a*b*x*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
238,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} + 2 c^{2} x^{2} + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**4 + 2*c**2*x**2 + 1), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**4 + 2*c**2*x**2 + 1), x))/d**2","F",0
239,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2}}{c^{4} x^{5} + 2 c^{2} x^{3} + x}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{5} + 2 c^{2} x^{3} + x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{5} + 2 c^{2} x^{3} + x}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**4*x**5 + 2*c**2*x**3 + x), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**5 + 2*c**2*x**3 + x), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**5 + 2*c**2*x**3 + x), x))/d**2","F",0
240,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2}}{c^{4} x^{6} + 2 c^{2} x^{4} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{6} + 2 c^{2} x^{4} + x^{2}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{6} + 2 c^{2} x^{4} + x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**4*x**6 + 2*c**2*x**4 + x**2), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**6 + 2*c**2*x**4 + x**2), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**6 + 2*c**2*x**4 + x**2), x))/d**2","F",0
241,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2}}{c^{4} x^{7} + 2 c^{2} x^{5} + x^{3}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{7} + 2 c^{2} x^{5} + x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{7} + 2 c^{2} x^{5} + x^{3}}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**4*x**7 + 2*c**2*x**5 + x**3), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**7 + 2*c**2*x**5 + x**3), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**7 + 2*c**2*x**5 + x**3), x))/d**2","F",0
242,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d)**2,x)","\frac{\int \frac{a^{2}}{c^{4} x^{8} + 2 c^{2} x^{6} + x^{4}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{8} + 2 c^{2} x^{6} + x^{4}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{8} + 2 c^{2} x^{6} + x^{4}}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**4*x**8 + 2*c**2*x**6 + x**4), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**8 + 2*c**2*x**6 + x**4), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**8 + 2*c**2*x**6 + x**4), x))/d**2","F",0
243,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2} x^{4}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{4} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{4} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**4/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b**2*x**4*asinh(c*x)**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(2*a*b*x**4*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
244,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2} x^{3}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**3/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b**2*x**3*asinh(c*x)**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(2*a*b*x**3*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
245,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2} x^{2}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b**2*x**2*asinh(c*x)**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(2*a*b*x**2*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
246,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2} x}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} x \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b x \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b**2*x*asinh(c*x)**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(2*a*b*x*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
247,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{6} + 3 c^{4} x^{4} + 3 c^{2} x^{2} + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(b**2*asinh(c*x)**2/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x) + Integral(2*a*b*asinh(c*x)/(c**6*x**6 + 3*c**4*x**4 + 3*c**2*x**2 + 1), x))/d**3","F",0
248,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2}}{c^{6} x^{7} + 3 c^{4} x^{5} + 3 c^{2} x^{3} + x}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{7} + 3 c^{4} x^{5} + 3 c^{2} x^{3} + x}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{7} + 3 c^{4} x^{5} + 3 c^{2} x^{3} + x}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**6*x**7 + 3*c**4*x**5 + 3*c**2*x**3 + x), x) + Integral(b**2*asinh(c*x)**2/(c**6*x**7 + 3*c**4*x**5 + 3*c**2*x**3 + x), x) + Integral(2*a*b*asinh(c*x)/(c**6*x**7 + 3*c**4*x**5 + 3*c**2*x**3 + x), x))/d**3","F",0
249,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2}}{c^{6} x^{8} + 3 c^{4} x^{6} + 3 c^{2} x^{4} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{8} + 3 c^{4} x^{6} + 3 c^{2} x^{4} + x^{2}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{8} + 3 c^{4} x^{6} + 3 c^{2} x^{4} + x^{2}}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**6*x**8 + 3*c**4*x**6 + 3*c**2*x**4 + x**2), x) + Integral(b**2*asinh(c*x)**2/(c**6*x**8 + 3*c**4*x**6 + 3*c**2*x**4 + x**2), x) + Integral(2*a*b*asinh(c*x)/(c**6*x**8 + 3*c**4*x**6 + 3*c**2*x**4 + x**2), x))/d**3","F",0
250,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**6*x**9 + 3*c**4*x**7 + 3*c**2*x**5 + x**3), x) + Integral(b**2*asinh(c*x)**2/(c**6*x**9 + 3*c**4*x**7 + 3*c**2*x**5 + x**3), x) + Integral(2*a*b*asinh(c*x)/(c**6*x**9 + 3*c**4*x**7 + 3*c**2*x**5 + x**3), x))/d**3","F",0
251,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d)**3,x)","\frac{\int \frac{a^{2}}{c^{6} x^{10} + 3 c^{4} x^{8} + 3 c^{2} x^{6} + x^{4}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{6} x^{10} + 3 c^{4} x^{8} + 3 c^{2} x^{6} + x^{4}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{6} x^{10} + 3 c^{4} x^{8} + 3 c^{2} x^{6} + x^{4}}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**6*x**10 + 3*c**4*x**8 + 3*c**2*x**6 + x**4), x) + Integral(b**2*asinh(c*x)**2/(c**6*x**10 + 3*c**4*x**8 + 3*c**2*x**6 + x**4), x) + Integral(2*a*b*asinh(c*x)/(c**6*x**10 + 3*c**4*x**8 + 3*c**2*x**6 + x**4), x))/d**3","F",0
252,-1,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,1,405,0,95.261805," ","integrate((pi*c**2*x**2+pi)**(3/2)*(a+b*asinh(c*x))**2,x)","\begin{cases} \frac{\pi^{\frac{3}{2}} a^{2} c^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{4} + \frac{5 \pi^{\frac{3}{2}} a^{2} x \sqrt{c^{2} x^{2} + 1}}{8} + \frac{3 \pi^{\frac{3}{2}} a^{2} \operatorname{asinh}{\left(c x \right)}}{8 c} - \frac{\pi^{\frac{3}{2}} a b c^{3} x^{4}}{8} + \frac{\pi^{\frac{3}{2}} a b c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{2} - \frac{5 \pi^{\frac{3}{2}} a b c x^{2}}{8} + \frac{5 \pi^{\frac{3}{2}} a b x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{4} + \frac{3 \pi^{\frac{3}{2}} a b \operatorname{asinh}^{2}{\left(c x \right)}}{8 c} - \frac{\pi^{\frac{3}{2}} b^{2} c^{3} x^{4} \operatorname{asinh}{\left(c x \right)}}{8} + \frac{\pi^{\frac{3}{2}} b^{2} c^{2} x^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(c x \right)}}{4} + \frac{\pi^{\frac{3}{2}} b^{2} c^{2} x^{3} \sqrt{c^{2} x^{2} + 1}}{32} - \frac{5 \pi^{\frac{3}{2}} b^{2} c x^{2} \operatorname{asinh}{\left(c x \right)}}{8} + \frac{5 \pi^{\frac{3}{2}} b^{2} x \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(c x \right)}}{8} + \frac{17 \pi^{\frac{3}{2}} b^{2} x \sqrt{c^{2} x^{2} + 1}}{64} + \frac{\pi^{\frac{3}{2}} b^{2} \operatorname{asinh}^{3}{\left(c x \right)}}{8 c} - \frac{17 \pi^{\frac{3}{2}} b^{2} \operatorname{asinh}{\left(c x \right)}}{64 c} & \text{for}\: c \neq 0 \\\pi^{\frac{3}{2}} a^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((pi**(3/2)*a**2*c**2*x**3*sqrt(c**2*x**2 + 1)/4 + 5*pi**(3/2)*a**2*x*sqrt(c**2*x**2 + 1)/8 + 3*pi**(3/2)*a**2*asinh(c*x)/(8*c) - pi**(3/2)*a*b*c**3*x**4/8 + pi**(3/2)*a*b*c**2*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/2 - 5*pi**(3/2)*a*b*c*x**2/8 + 5*pi**(3/2)*a*b*x*sqrt(c**2*x**2 + 1)*asinh(c*x)/4 + 3*pi**(3/2)*a*b*asinh(c*x)**2/(8*c) - pi**(3/2)*b**2*c**3*x**4*asinh(c*x)/8 + pi**(3/2)*b**2*c**2*x**3*sqrt(c**2*x**2 + 1)*asinh(c*x)**2/4 + pi**(3/2)*b**2*c**2*x**3*sqrt(c**2*x**2 + 1)/32 - 5*pi**(3/2)*b**2*c*x**2*asinh(c*x)/8 + 5*pi**(3/2)*b**2*x*sqrt(c**2*x**2 + 1)*asinh(c*x)**2/8 + 17*pi**(3/2)*b**2*x*sqrt(c**2*x**2 + 1)/64 + pi**(3/2)*b**2*asinh(c*x)**3/(8*c) - 17*pi**(3/2)*b**2*asinh(c*x)/(64*c), Ne(c, 0)), (pi**(3/2)*a**2*x, True))","A",0
254,0,0,0,0.000000," ","integrate((pi*c**2*x**2+pi)**(1/2)*(a+b*asinh(c*x))**2,x)","\sqrt{\pi} \left(\int a^{2} \sqrt{c^{2} x^{2} + 1}\, dx + \int b^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(c x \right)}\, dx + \int 2 a b \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}\, dx\right)"," ",0,"sqrt(pi)*(Integral(a**2*sqrt(c**2*x**2 + 1), x) + Integral(b**2*sqrt(c**2*x**2 + 1)*asinh(c*x)**2, x) + Integral(2*a*b*sqrt(c**2*x**2 + 1)*asinh(c*x), x))","F",0
255,1,88,0,2.809421," ","integrate((a+b*asinh(c*x))**2/(pi*c**2*x**2+pi)**(1/2),x)","\begin{cases} a^{2} \left(\begin{cases} \frac{\sqrt{- \frac{1}{c^{2}}} \operatorname{asin}{\left(x \sqrt{- c^{2}} \right)}}{\sqrt{\pi}} & \text{for}\: \pi c^{2} < 0 \\\frac{\sqrt{\frac{1}{c^{2}}} \operatorname{asinh}{\left(x \sqrt{c^{2}} \right)}}{\sqrt{\pi}} & \text{for}\: \pi c^{2} > 0 \end{cases}\right) & \text{for}\: b = 0 \\\frac{a^{2} x}{\sqrt{\pi}} & \text{for}\: c = 0 \\\frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{3}}{3 \sqrt{\pi} b c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*Piecewise((sqrt(-1/c**2)*asin(x*sqrt(-c**2))/sqrt(pi), pi*c**2 < 0), (sqrt(c**(-2))*asinh(x*sqrt(c**2))/sqrt(pi), pi*c**2 > 0)), Eq(b, 0)), (a**2*x/sqrt(pi), Eq(c, 0)), ((a + b*asinh(c*x))**3/(3*sqrt(pi)*b*c), True))","A",0
256,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(pi*c**2*x**2+pi)**(3/2),x)","\frac{\int \frac{a^{2}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{3}{2}}}"," ",0,"(Integral(a**2/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b**2*asinh(c*x)**2/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(2*a*b*asinh(c*x)/(c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(3/2)","F",0
257,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(pi*c**2*x**2+pi)**(5/2),x)","\frac{\int \frac{a^{2}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{b^{2} \operatorname{asinh}^{2}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx + \int \frac{2 a b \operatorname{asinh}{\left(c x \right)}}{c^{4} x^{4} \sqrt{c^{2} x^{2} + 1} + 2 c^{2} x^{2} \sqrt{c^{2} x^{2} + 1} + \sqrt{c^{2} x^{2} + 1}}\, dx}{\pi^{\frac{5}{2}}}"," ",0,"(Integral(a**2/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(b**2*asinh(c*x)**2/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x) + Integral(2*a*b*asinh(c*x)/(c**4*x**4*sqrt(c**2*x**2 + 1) + 2*c**2*x**2*sqrt(c**2*x**2 + 1) + sqrt(c**2*x**2 + 1)), x))/pi**(5/2)","F",0
258,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2),x)","\int x^{3} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**3*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2, x)","F",0
259,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2),x)","\int x^{2} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2, x)","F",0
260,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2),x)","\int x \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2, x)","F",0
261,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(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)^{2}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2, x)","F",0
262,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2)/x,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2/x, x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2)/x**2,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2/x**2, x)","F",0
264,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2)/x**3,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2/x**3, x)","F",0
265,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(c**2*d*x**2+d)**(1/2)/x**4,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2/x**4, x)","F",0
266,0,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2,x)","\int x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**3*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2, x)","F",0
267,0,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2,x)","\int x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2, x)","F",0
268,0,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2,x)","\int x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x*(d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2, x)","F",0
269,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2,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)^{2}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2, x)","F",0
270,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2/x,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)^{2}}{x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2/x, x)","F",0
271,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2/x**2,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)^{2}}{x^{2}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2/x**2, x)","F",0
272,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2/x**3,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)^{2}}{x^{3}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2/x**3, x)","F",0
273,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2/x**4,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)^{2}}{x^{4}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**2/x**4, x)","F",0
274,-1,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,0,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2,x)","\int x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x*(d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2, x)","F",0
277,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2,x)","\int \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2, x)","F",0
278,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2/x,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)^{2}}{x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2/x, x)","F",0
279,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2/x**2,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)^{2}}{x^{2}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2/x**2, x)","F",0
280,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2/x**3,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)^{2}}{x^{3}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2/x**3, x)","F",0
281,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2/x**4,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)^{2}}{x^{4}}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(5/2)*(a + b*asinh(c*x))**2/x**4, x)","F",0
282,1,146,0,3.684572," ","integrate(x**4*asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{4} \operatorname{asinh}{\left(a x \right)}}{8 a} + \frac{x^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{4 a^{2}} + \frac{x^{3} \sqrt{a^{2} x^{2} + 1}}{32 a^{2}} + \frac{3 x^{2} \operatorname{asinh}{\left(a x \right)}}{8 a^{3}} - \frac{3 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{8 a^{4}} - \frac{15 x \sqrt{a^{2} x^{2} + 1}}{64 a^{4}} + \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{8 a^{5}} + \frac{15 \operatorname{asinh}{\left(a x \right)}}{64 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**4*asinh(a*x)/(8*a) + x**3*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(4*a**2) + x**3*sqrt(a**2*x**2 + 1)/(32*a**2) + 3*x**2*asinh(a*x)/(8*a**3) - 3*x*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(8*a**4) - 15*x*sqrt(a**2*x**2 + 1)/(64*a**4) + asinh(a*x)**3/(8*a**5) + 15*asinh(a*x)/(64*a**5), Ne(a, 0)), (0, True))","A",0
283,1,121,0,2.173159," ","integrate(x**3*asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{2 x^{3} \operatorname{asinh}{\left(a x \right)}}{9 a} + \frac{x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{3 a^{2}} + \frac{2 x^{2} \sqrt{a^{2} x^{2} + 1}}{27 a^{2}} + \frac{4 x \operatorname{asinh}{\left(a x \right)}}{3 a^{3}} - \frac{2 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{3 a^{4}} - \frac{40 \sqrt{a^{2} x^{2} + 1}}{27 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x**3*asinh(a*x)/(9*a) + x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(3*a**2) + 2*x**2*sqrt(a**2*x**2 + 1)/(27*a**2) + 4*x*asinh(a*x)/(3*a**3) - 2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(3*a**4) - 40*sqrt(a**2*x**2 + 1)/(27*a**4), Ne(a, 0)), (0, True))","A",0
284,1,78,0,1.237190," ","integrate(x**2*asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{2} \operatorname{asinh}{\left(a x \right)}}{2 a} + \frac{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{2 a^{2}} + \frac{x \sqrt{a^{2} x^{2} + 1}}{4 a^{2}} - \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{6 a^{3}} - \frac{\operatorname{asinh}{\left(a x \right)}}{4 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**2*asinh(a*x)/(2*a) + x*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(2*a**2) + x*sqrt(a**2*x**2 + 1)/(4*a**2) - asinh(a*x)**3/(6*a**3) - asinh(a*x)/(4*a**3), Ne(a, 0)), (0, True))","A",0
285,1,49,0,0.722602," ","integrate(x*asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{2 x \operatorname{asinh}{\left(a x \right)}}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{a^{2}} + \frac{2 \sqrt{a^{2} x^{2} + 1}}{a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*x*asinh(a*x)/a + sqrt(a**2*x**2 + 1)*asinh(a*x)**2/a**2 + 2*sqrt(a**2*x**2 + 1)/a**2, Ne(a, 0)), (0, True))","A",0
286,1,10,0,0.395334," ","integrate(asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{3 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a*x)**3/(3*a), Ne(a, 0)), (0, True))","A",0
287,0,0,0,0.000000," ","integrate(asinh(a*x)**2/x/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{x \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**2/(x*sqrt(a**2*x**2 + 1)), x)","F",0
288,0,0,0,0.000000," ","integrate(asinh(a*x)**2/x**2/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**2/(x**2*sqrt(a**2*x**2 + 1)), x)","F",0
289,0,0,0,0.000000," ","integrate(asinh(a*x)**2/x**3/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**2/(x**3*sqrt(a**2*x**2 + 1)), x)","F",0
290,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
291,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
292,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
293,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
294,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
295,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
296,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x*sqrt(d*(c**2*x**2 + 1))), x)","F",0
297,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{2} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**2*sqrt(d*(c**2*x**2 + 1))), x)","F",0
298,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{3} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**3*sqrt(d*(c**2*x**2 + 1))), x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{4} \sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**4*sqrt(d*(c**2*x**2 + 1))), x)","F",0
300,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
301,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
302,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
303,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
305,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
306,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**2*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
308,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**3*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
309,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{4} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**4*(d*(c**2*x**2 + 1))**(3/2)), x)","F",0
310,0,0,0,0.000000," ","integrate(x**5*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
311,0,0,0,0.000000," ","integrate(x**4*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
312,0,0,0,0.000000," ","integrate(x**3*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
313,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
314,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(5/2), x)","F",0
316,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x/(c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
317,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**2/(c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{2} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**2*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**3/(c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{3} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**3*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/x**4/(c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{x^{4} \left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(x**4*(d*(c**2*x**2 + 1))**(5/2)), x)","F",0
320,0,0,0,0.000000," ","integrate(asinh(a*x)**2/(a**2*c*x**2+c)**(7/2),x)","\int \frac{\operatorname{asinh}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(asinh(a*x)**2/(c*(a**2*x**2 + 1))**(7/2), x)","F",0
321,-1,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,0,0,0,0.000000," ","integrate(x**m*(c**2*d*x**2+d)**(1/2)*(a+b*asinh(c*x))**2,x)","\int x^{m} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**m*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**2, x)","F",0
324,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(1/2),x)","\int \frac{x^{m} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*(a + b*asinh(c*x))**2/sqrt(d*(c**2*x**2 + 1)), x)","F",0
325,0,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(3/2),x)","\int \frac{x^{m} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d \left(c^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*(a + b*asinh(c*x))**2/(d*(c**2*x**2 + 1))**(3/2), x)","F",0
326,-1,0,0,0.000000," ","integrate(x**m*(a+b*asinh(c*x))**2/(c**2*d*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,0,0,0,0.000000," ","integrate(x**m*asinh(a*x)**2/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{m} \operatorname{asinh}^{2}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m*asinh(a*x)**2/sqrt(a**2*x**2 + 1), x)","F",0
328,1,355,0,18.410069," ","integrate((a**2*c*x**2+c)**3*asinh(a*x)**3,x)","\begin{cases} \frac{a^{6} c^{3} x^{7} \operatorname{asinh}^{3}{\left(a x \right)}}{7} + \frac{6 a^{6} c^{3} x^{7} \operatorname{asinh}{\left(a x \right)}}{343} - \frac{3 a^{5} c^{3} x^{6} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{49} - \frac{6 a^{5} c^{3} x^{6} \sqrt{a^{2} x^{2} + 1}}{2401} + \frac{3 a^{4} c^{3} x^{5} \operatorname{asinh}^{3}{\left(a x \right)}}{5} + \frac{702 a^{4} c^{3} x^{5} \operatorname{asinh}{\left(a x \right)}}{6125} - \frac{351 a^{3} c^{3} x^{4} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{1225} - \frac{29898 a^{3} c^{3} x^{4} \sqrt{a^{2} x^{2} + 1}}{1500625} + a^{2} c^{3} x^{3} \operatorname{asinh}^{3}{\left(a x \right)} + \frac{1514 a^{2} c^{3} x^{3} \operatorname{asinh}{\left(a x \right)}}{3675} - \frac{757 a c^{3} x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{1225} - \frac{1495874 a c^{3} x^{2} \sqrt{a^{2} x^{2} + 1}}{13505625} + c^{3} x \operatorname{asinh}^{3}{\left(a x \right)} + \frac{4322 c^{3} x \operatorname{asinh}{\left(a x \right)}}{1225} - \frac{2161 c^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{1225 a} - \frac{44658302 c^{3} \sqrt{a^{2} x^{2} + 1}}{13505625 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**7*asinh(a*x)**3/7 + 6*a**6*c**3*x**7*asinh(a*x)/343 - 3*a**5*c**3*x**6*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/49 - 6*a**5*c**3*x**6*sqrt(a**2*x**2 + 1)/2401 + 3*a**4*c**3*x**5*asinh(a*x)**3/5 + 702*a**4*c**3*x**5*asinh(a*x)/6125 - 351*a**3*c**3*x**4*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/1225 - 29898*a**3*c**3*x**4*sqrt(a**2*x**2 + 1)/1500625 + a**2*c**3*x**3*asinh(a*x)**3 + 1514*a**2*c**3*x**3*asinh(a*x)/3675 - 757*a*c**3*x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/1225 - 1495874*a*c**3*x**2*sqrt(a**2*x**2 + 1)/13505625 + c**3*x*asinh(a*x)**3 + 4322*c**3*x*asinh(a*x)/1225 - 2161*c**3*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(1225*a) - 44658302*c**3*sqrt(a**2*x**2 + 1)/(13505625*a), Ne(a, 0)), (0, True))","A",0
329,1,262,0,6.633537," ","integrate((a**2*c*x**2+c)**2*asinh(a*x)**3,x)","\begin{cases} \frac{a^{4} c^{2} x^{5} \operatorname{asinh}^{3}{\left(a x \right)}}{5} + \frac{6 a^{4} c^{2} x^{5} \operatorname{asinh}{\left(a x \right)}}{125} - \frac{3 a^{3} c^{2} x^{4} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{25} - \frac{6 a^{3} c^{2} x^{4} \sqrt{a^{2} x^{2} + 1}}{625} + \frac{2 a^{2} c^{2} x^{3} \operatorname{asinh}^{3}{\left(a x \right)}}{3} + \frac{76 a^{2} c^{2} x^{3} \operatorname{asinh}{\left(a x \right)}}{225} - \frac{38 a c^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{75} - \frac{1684 a c^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{16875} + c^{2} x \operatorname{asinh}^{3}{\left(a x \right)} + \frac{298 c^{2} x \operatorname{asinh}{\left(a x \right)}}{75} - \frac{149 c^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{75 a} - \frac{63682 c^{2} \sqrt{a^{2} x^{2} + 1}}{16875 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**5*asinh(a*x)**3/5 + 6*a**4*c**2*x**5*asinh(a*x)/125 - 3*a**3*c**2*x**4*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/25 - 6*a**3*c**2*x**4*sqrt(a**2*x**2 + 1)/625 + 2*a**2*c**2*x**3*asinh(a*x)**3/3 + 76*a**2*c**2*x**3*asinh(a*x)/225 - 38*a*c**2*x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/75 - 1684*a*c**2*x**2*sqrt(a**2*x**2 + 1)/16875 + c**2*x*asinh(a*x)**3 + 298*c**2*x*asinh(a*x)/75 - 149*c**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(75*a) - 63682*c**2*sqrt(a**2*x**2 + 1)/(16875*a), Ne(a, 0)), (0, True))","A",0
330,1,150,0,2.084491," ","integrate((a**2*c*x**2+c)*asinh(a*x)**3,x)","\begin{cases} \frac{a^{2} c x^{3} \operatorname{asinh}^{3}{\left(a x \right)}}{3} + \frac{2 a^{2} c x^{3} \operatorname{asinh}{\left(a x \right)}}{9} - \frac{a c x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{3} - \frac{2 a c x^{2} \sqrt{a^{2} x^{2} + 1}}{27} + c x \operatorname{asinh}^{3}{\left(a x \right)} + \frac{14 c x \operatorname{asinh}{\left(a x \right)}}{3} - \frac{7 c \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{2}{\left(a x \right)}}{3 a} - \frac{122 c \sqrt{a^{2} x^{2} + 1}}{27 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**3*asinh(a*x)**3/3 + 2*a**2*c*x**3*asinh(a*x)/9 - a*c*x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/3 - 2*a*c*x**2*sqrt(a**2*x**2 + 1)/27 + c*x*asinh(a*x)**3 + 14*c*x*asinh(a*x)/3 - 7*c*sqrt(a**2*x**2 + 1)*asinh(a*x)**2/(3*a) - 122*c*sqrt(a**2*x**2 + 1)/(27*a), Ne(a, 0)), (0, True))","A",0
331,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(asinh(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
332,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(asinh(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
333,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(asinh(a*x)**3/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
334,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*asinh(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*asinh(a*x)**3,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{asinh}^{3}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*asinh(a*x)**3, x)","F",0
336,0,0,0,0.000000," ","integrate(asinh(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{asinh}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*asinh(a*x)**3, x)","F",0
337,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(asinh(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
338,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(asinh(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
340,0,0,0,0.000000," ","integrate(asinh(a*x)**3/(a**2*c*x**2+c)**(7/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(asinh(a*x)**3/(c*(a**2*x**2 + 1))**(7/2), x)","F",0
341,0,0,0,0.000000," ","integrate(x**m*asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{m} \operatorname{asinh}^{3}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m*asinh(a*x)**3/sqrt(a**2*x**2 + 1), x)","F",0
342,1,185,0,6.470115," ","integrate(x**4*asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{3 x^{4} \operatorname{asinh}^{2}{\left(a x \right)}}{16 a} - \frac{3 x^{4}}{128 a} + \frac{x^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{4 a^{2}} + \frac{3 x^{3} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{32 a^{2}} + \frac{9 x^{2} \operatorname{asinh}^{2}{\left(a x \right)}}{16 a^{3}} + \frac{45 x^{2}}{128 a^{3}} - \frac{3 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{8 a^{4}} - \frac{45 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{64 a^{4}} + \frac{3 \operatorname{asinh}^{4}{\left(a x \right)}}{32 a^{5}} + \frac{45 \operatorname{asinh}^{2}{\left(a x \right)}}{128 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*x**4*asinh(a*x)**2/(16*a) - 3*x**4/(128*a) + x**3*sqrt(a**2*x**2 + 1)*asinh(a*x)**3/(4*a**2) + 3*x**3*sqrt(a**2*x**2 + 1)*asinh(a*x)/(32*a**2) + 9*x**2*asinh(a*x)**2/(16*a**3) + 45*x**2/(128*a**3) - 3*x*sqrt(a**2*x**2 + 1)*asinh(a*x)**3/(8*a**4) - 45*x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(64*a**4) + 3*asinh(a*x)**4/(32*a**5) + 45*asinh(a*x)**2/(128*a**5), Ne(a, 0)), (0, True))","A",0
343,1,148,0,3.573319," ","integrate(x**3*asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{x^{3} \operatorname{asinh}^{2}{\left(a x \right)}}{3 a} - \frac{2 x^{3}}{27 a} + \frac{x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{3 a^{2}} + \frac{2 x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{9 a^{2}} + \frac{2 x \operatorname{asinh}^{2}{\left(a x \right)}}{a^{3}} + \frac{40 x}{9 a^{3}} - \frac{2 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{3 a^{4}} - \frac{40 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{9 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**3*asinh(a*x)**2/(3*a) - 2*x**3/(27*a) + x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)**3/(3*a**2) + 2*x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)/(9*a**2) + 2*x*asinh(a*x)**2/a**3 + 40*x/(9*a**3) - 2*sqrt(a**2*x**2 + 1)*asinh(a*x)**3/(3*a**4) - 40*sqrt(a**2*x**2 + 1)*asinh(a*x)/(9*a**4), Ne(a, 0)), (0, True))","A",0
344,1,100,0,2.197481," ","integrate(x**2*asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{3 x^{2} \operatorname{asinh}^{2}{\left(a x \right)}}{4 a} - \frac{3 x^{2}}{8 a} + \frac{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{2 a^{2}} + \frac{3 x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{4 a^{2}} - \frac{\operatorname{asinh}^{4}{\left(a x \right)}}{8 a^{3}} - \frac{3 \operatorname{asinh}^{2}{\left(a x \right)}}{8 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*x**2*asinh(a*x)**2/(4*a) - 3*x**2/(8*a) + x*sqrt(a**2*x**2 + 1)*asinh(a*x)**3/(2*a**2) + 3*x*sqrt(a**2*x**2 + 1)*asinh(a*x)/(4*a**2) - asinh(a*x)**4/(8*a**3) - 3*asinh(a*x)**2/(8*a**3), Ne(a, 0)), (0, True))","A",0
345,1,61,0,1.187720," ","integrate(x*asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{3 x \operatorname{asinh}^{2}{\left(a x \right)}}{a} - \frac{6 x}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}^{3}{\left(a x \right)}}{a^{2}} + \frac{6 \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}{a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*x*asinh(a*x)**2/a - 6*x/a + sqrt(a**2*x**2 + 1)*asinh(a*x)**3/a**2 + 6*sqrt(a**2*x**2 + 1)*asinh(a*x)/a**2, Ne(a, 0)), (0, True))","A",0
346,1,10,0,0.682314," ","integrate(asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asinh}^{4}{\left(a x \right)}}{4 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((asinh(a*x)**4/(4*a), Ne(a, 0)), (0, True))","A",0
347,0,0,0,0.000000," ","integrate(asinh(a*x)**3/x/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{x \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**3/(x*sqrt(a**2*x**2 + 1)), x)","F",0
348,0,0,0,0.000000," ","integrate(asinh(a*x)**3/x**2/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**3/(x**2*sqrt(a**2*x**2 + 1)), x)","F",0
349,0,0,0,0.000000," ","integrate(asinh(a*x)**3/x**3/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{3}{\left(a x \right)}}{x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**3/(x**3*sqrt(a**2*x**2 + 1)), x)","F",0
350,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/asinh(a*x),x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/asinh(a*x), x) + Integral(3*a**4*x**4/asinh(a*x), x) + Integral(a**6*x**6/asinh(a*x), x) + Integral(1/asinh(a*x), x))","F",0
351,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/asinh(a*x),x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/asinh(a*x), x) + Integral(a**4*x**4/asinh(a*x), x) + Integral(1/asinh(a*x), x))","F",0
352,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/asinh(a*x),x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{asinh}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/asinh(a*x), x) + Integral(1/asinh(a*x), x))","F",0
353,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/asinh(a*x),x)","\frac{\int \frac{1}{a^{2} x^{2} \operatorname{asinh}{\left(a x \right)} + \operatorname{asinh}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**2*asinh(a*x) + asinh(a*x)), x)/c","F",0
354,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/asinh(a*x),x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{asinh}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{asinh}{\left(a x \right)} + \operatorname{asinh}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*asinh(a*x) + 2*a**2*x**2*asinh(a*x) + asinh(a*x)), x)/c**2","F",0
355,0,0,0,0.000000," ","integrate(x**4*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{4} \sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**4*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
356,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{3} \sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**3*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
357,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{2} \sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
358,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x \sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
359,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
360,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x*(a + b*asinh(c*x))), x)","F",0
361,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**2/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**2*(a + b*asinh(c*x))), x)","F",0
362,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**3/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**3*(a + b*asinh(c*x))), x)","F",0
363,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**4/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**4*(a + b*asinh(c*x))), x)","F",0
364,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{3} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**3*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x)), x)","F",0
365,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**2*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x)), x)","F",0
366,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x)), x)","F",0
367,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x)), x)","F",0
368,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x*(a + b*asinh(c*x))), x)","F",0
369,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**2/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**2*(a + b*asinh(c*x))), x)","F",0
370,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**3/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**3*(a + b*asinh(c*x))), x)","F",0
371,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**4/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**4*(a + b*asinh(c*x))), x)","F",0
372,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{3} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**3*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x)), x)","F",0
373,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**2*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x)), x)","F",0
374,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x)),x)","\int \frac{x \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x)), x)","F",0
375,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x)), x)","F",0
376,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x*(a + b*asinh(c*x))), x)","F",0
377,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**2/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**2*(a + b*asinh(c*x))), x)","F",0
378,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**3/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**3*(a + b*asinh(c*x))), x)","F",0
379,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**4/(a+b*asinh(c*x)),x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**4*(a + b*asinh(c*x))), x)","F",0
380,0,0,0,0.000000," ","integrate(x**4/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/(sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
381,0,0,0,0.000000," ","integrate(x**3/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/(sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
382,0,0,0,0.000000," ","integrate(x**2/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/(sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
383,0,0,0,0.000000," ","integrate(x**2/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/(sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
384,0,0,0,0.000000," ","integrate(x/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{x}{\sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
385,1,7,0,0.480898," ","integrate(1/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\frac{\log{\left(\operatorname{asinh}{\left(a x \right)} \right)}}{a}"," ",0,"log(asinh(a*x))/a","A",0
386,0,0,0,0.000000," ","integrate(1/x/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{1}{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/x**2/asinh(a*x)/(a**2*x**2+1)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a**2*x**2 + 1)*asinh(a*x)), x)","F",0
388,0,0,0,0.000000," ","integrate(x**5/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{5}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**5/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
389,0,0,0,0.000000," ","integrate(x**4/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{4}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**4/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
390,0,0,0,0.000000," ","integrate(x**3/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{3}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**3/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
391,0,0,0,0.000000," ","integrate(x**2/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**2/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
392,0,0,0,0.000000," ","integrate(x/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
393,1,26,0,1.505726," ","integrate(1/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\begin{cases} \frac{x}{a} & \text{for}\: c = 0 \wedge \left(b = 0 \vee c = 0\right) \\\frac{\operatorname{asinh}{\left(c x \right)}}{a c} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + \operatorname{asinh}{\left(c x \right)} \right)}}{b c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a, Eq(c, 0) & (Eq(b, 0) | Eq(c, 0))), (asinh(c*x)/(a*c), Eq(b, 0)), (log(a/b + asinh(c*x))/(b*c), True))","A",0
394,0,0,0,0.000000," ","integrate(1/x/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{1}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(1/(x*(a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
395,0,0,0,0.000000," ","integrate(1/x**2/(a+b*asinh(c*x))/(c**2*x**2+1)**(1/2),x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
396,0,0,0,0.000000," ","integrate(x**2/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
397,0,0,0,0.000000," ","integrate(x/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
398,0,0,0,0.000000," ","integrate(1/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
399,0,0,0,0.000000," ","integrate(1/x/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{1}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
400,0,0,0,0.000000," ","integrate(1/x**2/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
401,-1,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,0,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{m} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**m*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x)), x)","F",0
403,0,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{m} \sqrt{c^{2} x^{2} + 1}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x)), x)","F",0
404,0,0,0,0.000000," ","integrate(x**m/(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m/((a + b*asinh(c*x))*sqrt(c**2*x**2 + 1)), x)","F",0
405,0,0,0,0.000000," ","integrate(x**m/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{x^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m/((a + b*asinh(c*x))*(c**2*x**2 + 1)**(3/2)), x)","F",0
406,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/asinh(a*x)**2,x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/asinh(a*x)**2, x) + Integral(3*a**4*x**4/asinh(a*x)**2, x) + Integral(a**6*x**6/asinh(a*x)**2, x) + Integral(asinh(a*x)**(-2), x))","F",0
407,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/asinh(a*x)**2,x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/asinh(a*x)**2, x) + Integral(a**4*x**4/asinh(a*x)**2, x) + Integral(asinh(a*x)**(-2), x))","F",0
408,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/asinh(a*x)**2,x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{asinh}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/asinh(a*x)**2, x) + Integral(asinh(a*x)**(-2), x))","F",0
409,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/asinh(a*x)**2,x)","\frac{\int \frac{1}{a^{2} x^{2} \operatorname{asinh}^{2}{\left(a x \right)} + \operatorname{asinh}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**2*asinh(a*x)**2 + asinh(a*x)**2), x)/c","F",0
410,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/asinh(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{asinh}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{asinh}^{2}{\left(a x \right)} + \operatorname{asinh}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*asinh(a*x)**2 + 2*a**2*x**2*asinh(a*x)**2 + asinh(a*x)**2), x)/c**2","F",0
411,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{3} \sqrt{c^{2} x^{2} + 1}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x))**2, x)","F",0
412,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{2} \sqrt{c^{2} x^{2} + 1}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**2*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x))**2, x)","F",0
413,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x \sqrt{c^{2} x^{2} + 1}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x))**2, x)","F",0
414,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x))**2, x)","F",0
415,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x*(a + b*asinh(c*x))**2), x)","F",0
416,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**2/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**2*(a + b*asinh(c*x))**2), x)","F",0
417,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**3/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**3*(a + b*asinh(c*x))**2), x)","F",0
418,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/x**4/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/(x**4*(a + b*asinh(c*x))**2), x)","F",0
419,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{3} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x))**2, x)","F",0
420,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**2*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x))**2, x)","F",0
421,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x))**2, x)","F",0
422,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x))**2, x)","F",0
423,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x*(a + b*asinh(c*x))**2), x)","F",0
424,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**2/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**2*(a + b*asinh(c*x))**2), x)","F",0
425,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**3/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**3*(a + b*asinh(c*x))**2), x)","F",0
426,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(3/2)/x**4/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(3/2)/(x**4*(a + b*asinh(c*x))**2), x)","F",0
427,0,0,0,0.000000," ","integrate(x**3*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{3} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x))**2, x)","F",0
428,0,0,0,0.000000," ","integrate(x**2*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**2*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x))**2, x)","F",0
429,0,0,0,0.000000," ","integrate(x*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*(c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x))**2, x)","F",0
430,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(a + b*asinh(c*x))**2, x)","F",0
431,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x*(a + b*asinh(c*x))**2), x)","F",0
432,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**2/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**2*(a + b*asinh(c*x))**2), x)","F",0
433,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**3/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{3} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**3*(a + b*asinh(c*x))**2), x)","F",0
434,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(5/2)/x**4/(a+b*asinh(c*x))**2,x)","\int \frac{\left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}{x^{4} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((c**2*x**2 + 1)**(5/2)/(x**4*(a + b*asinh(c*x))**2), x)","F",0
435,0,0,0,0.000000," ","integrate(x**5/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{5}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**5/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
436,0,0,0,0.000000," ","integrate(x**4/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{4}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**4/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
437,0,0,0,0.000000," ","integrate(x**3/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{3}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**3/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
438,0,0,0,0.000000," ","integrate(x**2/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**2/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
439,0,0,0,0.000000," ","integrate(x/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
440,1,36,0,3.060027," ","integrate(1/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\begin{cases} \frac{x}{a^{2}} & \text{for}\: b = 0 \wedge c = 0 \\\frac{\operatorname{asinh}{\left(c x \right)}}{a^{2} c} & \text{for}\: b = 0 \\\frac{x}{a^{2}} & \text{for}\: c = 0 \\- \frac{1}{a b c + b^{2} c \operatorname{asinh}{\left(c x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**2, Eq(b, 0) & Eq(c, 0)), (asinh(c*x)/(a**2*c), Eq(b, 0)), (x/a**2, Eq(c, 0)), (-1/(a*b*c + b**2*c*asinh(c*x)), True))","A",0
441,0,0,0,0.000000," ","integrate(1/x/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{1}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(1/(x*(a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
442,0,0,0,0.000000," ","integrate(1/x**2/(a+b*asinh(c*x))**2/(c**2*x**2+1)**(1/2),x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
443,0,0,0,0.000000," ","integrate(x**3/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{3}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
444,0,0,0,0.000000," ","integrate(x**2/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
445,0,0,0,0.000000," ","integrate(x/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
446,0,0,0,0.000000," ","integrate(1/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
447,0,0,0,0.000000," ","integrate(1/x/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
448,0,0,0,0.000000," ","integrate(1/x**2/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
449,0,0,0,0.000000," ","integrate(x**3/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{3}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
450,0,0,0,0.000000," ","integrate(x**2/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
451,0,0,0,0.000000," ","integrate(x/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
452,0,0,0,0.000000," ","integrate(1/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
453,0,0,0,0.000000," ","integrate(1/x/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{x \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
454,0,0,0,0.000000," ","integrate(1/x**2/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
455,-1,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,0,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{m} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**m*(c**2*x**2 + 1)**(3/2)/(a + b*asinh(c*x))**2, x)","F",0
457,0,0,0,0.000000," ","integrate(x**m*(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{m} \sqrt{c^{2} x^{2} + 1}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**m*sqrt(c**2*x**2 + 1)/(a + b*asinh(c*x))**2, x)","F",0
458,0,0,0,0.000000," ","integrate(x**m/(c**2*x**2+1)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m/((a + b*asinh(c*x))**2*sqrt(c**2*x**2 + 1)), x)","F",0
459,0,0,0,0.000000," ","integrate(x**m/(c**2*x**2+1)**(3/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(3/2)), x)","F",0
460,0,0,0,0.000000," ","integrate(x**m/(c**2*x**2+1)**(5/2)/(a+b*asinh(c*x))**2,x)","\int \frac{x^{m}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \left(c^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**m/((a + b*asinh(c*x))**2*(c**2*x**2 + 1)**(5/2)), x)","F",0
461,1,12,0,0.985877," ","integrate(1/asinh(a*x)**3/(a**2*x**2+1)**(1/2),x)","- \frac{1}{2 a \operatorname{asinh}^{2}{\left(a x \right)}}"," ",0,"-1/(2*a*asinh(a*x)**2)","A",0
462,0,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","d \left(\int \frac{x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{2} x^{5}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d*(Integral(x**3/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**2*x**5/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
463,0,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","d \left(\int \frac{x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{2} x^{4}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d*(Integral(x**2/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**2*x**4/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
464,0,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","d \left(\int \frac{x}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{2} x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d*(Integral(x/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**2*x**3/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
465,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","d \left(\int \frac{c^{2} x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{1}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d*(Integral(c**2*x**2/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(1/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
466,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)/x/(a+b*asinh(c*x))**(3/2),x)","d \left(\int \frac{c^{2} x^{2}}{a x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{1}{a x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d*(Integral(c**2*x**2/(a*x*sqrt(a + b*asinh(c*x)) + b*x*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(1/(a*x*sqrt(a + b*asinh(c*x)) + b*x*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
467,0,0,0,0.000000," ","integrate(x**3*(c**2*d*x**2+d)**2/(a+b*asinh(c*x))**(3/2),x)","d^{2} \left(\int \frac{x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{2 c^{2} x^{5}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{4} x^{7}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d**2*(Integral(x**3/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(2*c**2*x**5/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**4*x**7/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
468,0,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**2/(a+b*asinh(c*x))**(3/2),x)","d^{2} \left(\int \frac{x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{2 c^{2} x^{4}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{4} x^{6}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d**2*(Integral(x**2/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(2*c**2*x**4/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**4*x**6/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
469,0,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**2/(a+b*asinh(c*x))**(3/2),x)","d^{2} \left(\int \frac{x}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{2 c^{2} x^{3}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{4} x^{5}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d**2*(Integral(x/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(2*c**2*x**3/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**4*x**5/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
470,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2/(a+b*asinh(c*x))**(3/2),x)","d^{2} \left(\int \frac{2 c^{2} x^{2}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{4} x^{4}}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{1}{a \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d**2*(Integral(2*c**2*x**2/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**4*x**4/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(1/(a*sqrt(a + b*asinh(c*x)) + b*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
471,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**2/x/(a+b*asinh(c*x))**(3/2),x)","d^{2} \left(\int \frac{2 c^{2} x^{2}}{a x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{c^{4} x^{4}}{a x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx + \int \frac{1}{a x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} + b x \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \operatorname{asinh}{\left(c x \right)}}\, dx\right)"," ",0,"d**2*(Integral(2*c**2*x**2/(a*x*sqrt(a + b*asinh(c*x)) + b*x*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(c**4*x**4/(a*x*sqrt(a + b*asinh(c*x)) + b*x*sqrt(a + b*asinh(c*x))*asinh(c*x)), x) + Integral(1/(a*x*sqrt(a + b*asinh(c*x)) + b*x*sqrt(a + b*asinh(c*x))*asinh(c*x)), x))","F",0
472,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*asinh(a*x)**(1/2),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*sqrt(asinh(a*x)), x)","F",0
473,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)*asinh(a*x)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{asinh}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*sqrt(asinh(a*x)), x)","F",0
474,0,0,0,0.000000," ","integrate(asinh(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(asinh(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
475,0,0,0,0.000000," ","integrate(asinh(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(asinh(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
476,0,0,0,0.000000," ","integrate(asinh(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(asinh(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
477,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*asinh(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,0,0,0,0.000000," ","integrate(asinh(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*asinh(a*x)**(3/2), x)","F",0
479,0,0,0,0.000000," ","integrate(asinh(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(asinh(a*x)**(3/2)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
480,0,0,0,0.000000," ","integrate(asinh(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
481,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*asinh(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(asinh(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(asinh(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(asinh(a*x)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,0,0,0,0.000000," ","integrate((a**2+x**2)**(3/2)*asinh(x/a)**(1/2),x)","\int \left(a^{2} + x^{2}\right)^{\frac{3}{2}} \sqrt{\operatorname{asinh}{\left(\frac{x}{a} \right)}}\, dx"," ",0,"Integral((a**2 + x**2)**(3/2)*sqrt(asinh(x/a)), x)","F",0
486,0,0,0,0.000000," ","integrate((a**2+x**2)**(1/2)*asinh(x/a)**(1/2),x)","\int \sqrt{a^{2} + x^{2}} \sqrt{\operatorname{asinh}{\left(\frac{x}{a} \right)}}\, dx"," ",0,"Integral(sqrt(a**2 + x**2)*sqrt(asinh(x/a)), x)","F",0
487,0,0,0,0.000000," ","integrate(asinh(x/a)**(1/2)/(a**2+x**2)**(1/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(\frac{x}{a} \right)}}}{\sqrt{a^{2} + x^{2}}}\, dx"," ",0,"Integral(sqrt(asinh(x/a))/sqrt(a**2 + x**2), x)","F",0
488,0,0,0,0.000000," ","integrate(asinh(x/a)**(1/2)/(a**2+x**2)**(3/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(\frac{x}{a} \right)}}}{\left(a^{2} + x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(asinh(x/a))/(a**2 + x**2)**(3/2), x)","F",0
489,0,0,0,0.000000," ","integrate(asinh(x/a)**(1/2)/(a**2+x**2)**(5/2),x)","\int \frac{\sqrt{\operatorname{asinh}{\left(\frac{x}{a} \right)}}}{\left(a^{2} + x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(asinh(x/a))/(a**2 + x**2)**(5/2), x)","F",0
490,-1,0,0,0.000000," ","integrate((a**2+x**2)**(3/2)*asinh(x/a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,0,0,0,0.000000," ","integrate(asinh(x/a)**(3/2)*(a**2+x**2)**(1/2),x)","\int \sqrt{a^{2} + x^{2}} \operatorname{asinh}^{\frac{3}{2}}{\left(\frac{x}{a} \right)}\, dx"," ",0,"Integral(sqrt(a**2 + x**2)*asinh(x/a)**(3/2), x)","F",0
492,0,0,0,0.000000," ","integrate(asinh(x/a)**(3/2)/(a**2+x**2)**(1/2),x)","\int \frac{\operatorname{asinh}^{\frac{3}{2}}{\left(\frac{x}{a} \right)}}{\sqrt{a^{2} + x^{2}}}\, dx"," ",0,"Integral(asinh(x/a)**(3/2)/sqrt(a**2 + x**2), x)","F",0
493,0,0,0,0.000000," ","integrate(asinh(x/a)**(3/2)/(a**2+x**2)**(3/2),x)","\int \frac{\operatorname{asinh}^{\frac{3}{2}}{\left(\frac{x}{a} \right)}}{\left(a^{2} + x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asinh(x/a)**(3/2)/(a**2 + x**2)**(3/2), x)","F",0
494,0,0,0,0.000000," ","integrate(x/(x**2+1)**(1/2)/asinh(x)**(1/2),x)","\int \frac{x}{\sqrt{x^{2} + 1} \sqrt{\operatorname{asinh}{\left(x \right)}}}\, dx"," ",0,"Integral(x/(sqrt(x**2 + 1)*sqrt(asinh(x))), x)","F",0
495,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/asinh(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/asinh(a*x)**(1/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{\operatorname{asinh}{\left(a x \right)}}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/sqrt(asinh(a*x)), x)","F",0
497,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/asinh(a*x)**(1/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\sqrt{\operatorname{asinh}{\left(a x \right)}}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/sqrt(asinh(a*x)), x)","F",0
498,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(1/2)/asinh(a*x)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{asinh}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*sqrt(asinh(a*x))), x)","F",0
499,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/asinh(a*x)**(1/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{asinh}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*sqrt(asinh(a*x))), x)","F",0
500,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/asinh(a*x)**(1/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{asinh}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(5/2)*sqrt(asinh(a*x))), x)","F",0
501,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/asinh(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/asinh(a*x)**(3/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/asinh(a*x)**(3/2), x)","F",0
503,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/asinh(a*x)**(3/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/asinh(a*x)**(3/2), x)","F",0
504,0,0,0,0.000000," ","integrate(1/asinh(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*asinh(a*x)**(3/2)), x)","F",0
505,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/asinh(a*x)**(3/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{asinh}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*asinh(a*x)**(3/2)), x)","F",0
506,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/asinh(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/asinh(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/asinh(a*x)**(5/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{asinh}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/asinh(a*x)**(5/2), x)","F",0
509,0,0,0,0.000000," ","integrate(1/asinh(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{asinh}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*asinh(a*x)**(5/2)), x)","F",0
510,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/asinh(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/asinh(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,0,0,0,0.000000," ","integrate(x**2*(a+b*asinh(c*x))**n*(c**2*d*x**2+d)**(1/2),x)","\int x^{2} \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{n}\, dx"," ",0,"Integral(x**2*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**n, x)","F",0
513,0,0,0,0.000000," ","integrate(x*(a+b*asinh(c*x))**n*(c**2*d*x**2+d)**(1/2),x)","\int x \sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{n}\, dx"," ",0,"Integral(x*sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**n, x)","F",0
514,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**n*(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)^{n}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**n, x)","F",0
515,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**n*(c**2*d*x**2+d)**(1/2)/x,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{n}}{x}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**n/x, x)","F",0
516,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**n*(c**2*d*x**2+d)**(1/2)/x**2,x)","\int \frac{\sqrt{d \left(c^{2} x^{2} + 1\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{n}}{x^{2}}\, dx"," ",0,"Integral(sqrt(d*(c**2*x**2 + 1))*(a + b*asinh(c*x))**n/x**2, x)","F",0
517,-1,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,0,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**n/x,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)^{n}}{x}\, dx"," ",0,"Integral((d*(c**2*x**2 + 1))**(3/2)*(a + b*asinh(c*x))**n/x, x)","F",0
521,-1,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(3/2)*(a+b*asinh(c*x))**n/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate(x**2*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,-1,0,0,0.000000," ","integrate(x*(c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,-1,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**n/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate((c**2*d*x**2+d)**(5/2)*(a+b*asinh(c*x))**n/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,0,0,0,0.000000," ","integrate(x**m*asinh(a*x)**n/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{m} \operatorname{asinh}^{n}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**m*asinh(a*x)**n/sqrt(a**2*x**2 + 1), x)","F",0
528,0,0,0,0.000000," ","integrate(x**3*asinh(a*x)**n/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{3} \operatorname{asinh}^{n}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**3*asinh(a*x)**n/sqrt(a**2*x**2 + 1), x)","F",0
529,0,0,0,0.000000," ","integrate(x**2*asinh(a*x)**n/(a**2*x**2+1)**(1/2),x)","\int \frac{x^{2} \operatorname{asinh}^{n}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x**2*asinh(a*x)**n/sqrt(a**2*x**2 + 1), x)","F",0
530,0,0,0,0.000000," ","integrate(x*asinh(a*x)**n/(a**2*x**2+1)**(1/2),x)","\int \frac{x \operatorname{asinh}^{n}{\left(a x \right)}}{\sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(x*asinh(a*x)**n/sqrt(a**2*x**2 + 1), x)","F",0
531,1,34,0,0.865711," ","integrate(asinh(a*x)**n/(a**2*x**2+1)**(1/2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge n = -1 \\0^{n} x & \text{for}\: a = 0 \\\frac{\log{\left(\operatorname{asinh}{\left(a x \right)} \right)}}{a} & \text{for}\: n = -1 \\\frac{\operatorname{asinh}{\left(a x \right)} \operatorname{asinh}^{n}{\left(a x \right)}}{a n + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(n, -1)), (0**n*x, Eq(a, 0)), (log(asinh(a*x))/a, Eq(n, -1)), (asinh(a*x)*asinh(a*x)**n/(a*n + a), True))","A",0
532,0,0,0,0.000000," ","integrate(asinh(a*x)**n/x/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{n}{\left(a x \right)}}{x \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**n/(x*sqrt(a**2*x**2 + 1)), x)","F",0
533,0,0,0,0.000000," ","integrate(asinh(a*x)**n/x**2/(a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{asinh}^{n}{\left(a x \right)}}{x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"Integral(asinh(a*x)**n/(x**2*sqrt(a**2*x**2 + 1)), x)","F",0
534,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))*(f-I*c*f*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,0,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))*(f-I*c*f*x)**(1/2),x)","\int \left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral((I*d*(c*x - I))**(3/2)*sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x)), x)","F",0
536,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(d+I*c*d*x)**(1/2)*(f-I*c*f*x)**(1/2),x)","\int \sqrt{i d \left(c x - i\right)} \sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x)), x)","F",0
537,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(1/2),x)","\int \frac{\sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{i d \left(c x - i\right)}}\, dx"," ",0,"Integral(sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))/sqrt(I*d*(c*x - I)), x)","F",0
538,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(3/2),x)","\int \frac{\sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))/(I*d*(c*x - I))**(3/2), x)","F",0
539,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(f-I*c*f*x)**(3/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(f-I*c*f*x)**(3/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))*(d+I*c*d*x)**(1/2),x)","\int \sqrt{i d \left(c x - i\right)} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(-I*f*(c*x + I))**(3/2)*(a + b*asinh(c*x)), x)","F",0
543,0,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(1/2),x)","\int \frac{\left(- i f \left(c x + i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{i d \left(c x - i\right)}}\, dx"," ",0,"Integral((-I*f*(c*x + I))**(3/2)*(a + b*asinh(c*x))/sqrt(I*d*(c*x - I)), x)","F",0
544,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(f-I*c*f*x)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(f-I*c*f*x)**(5/2)*(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))*(d+I*c*d*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,0,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(1/2),x)","\int \frac{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((I*d*(c*x - I))**(3/2)*(a + b*asinh(c*x))/sqrt(-I*f*(c*x + I)), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{\sqrt{i d \left(c x - i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(a + b*asinh(c*x))/sqrt(-I*f*(c*x + I)), x)","F",0
555,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{i d \left(c x - i\right)} \sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(sqrt(I*d*(c*x - I))*sqrt(-I*f*(c*x + I))), x)","F",0
556,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/((I*d*(c*x - I))**(3/2)*sqrt(-I*f*(c*x + I))), x)","F",0
557,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(i d \left(c x - i\right)\right)^{\frac{5}{2}} \sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/((I*d*(c*x - I))**(5/2)*sqrt(-I*f*(c*x + I))), x)","F",0
558,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(3/2),x)","\int \frac{\sqrt{i d \left(c x - i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)}{\left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(a + b*asinh(c*x))/(-I*f*(c*x + I))**(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(f-I*c*f*x)**(3/2)/(d+I*c*d*x)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{i d \left(c x - i\right)} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(sqrt(I*d*(c*x - I))*(-I*f*(c*x + I))**(3/2)), x)","F",0
562,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/((I*d*(c*x - I))**(3/2)*(-I*f*(c*x + I))**(3/2)), x)","F",0
563,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(f-I*c*f*x)**(5/2)/(d+I*c*d*x)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{i d \left(c x - i\right)} \left(- i f \left(c x + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(sqrt(I*d*(c*x - I))*(-I*f*(c*x + I))**(5/2)), x)","F",0
568,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))**2*(f-I*c*f*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,0,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))**2*(f-I*c*f*x)**(1/2),x)","\int \left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((I*d*(c*x - I))**(3/2)*sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))**2, x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2)*(f-I*c*f*x)**(1/2),x)","\int \sqrt{i d \left(c x - i\right)} \sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))**2, x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(1/2),x)","\int \frac{\sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{i d \left(c x - i\right)}}\, dx"," ",0,"Integral(sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))**2/sqrt(I*d*(c*x - I)), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(3/2),x)","\int \frac{\sqrt{- i f \left(c x + i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-I*f*(c*x + I))*(a + b*asinh(c*x))**2/(I*d*(c*x - I))**(3/2), x)","F",0
575,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(f-I*c*f*x)**(1/2)/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,0,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2),x)","\int \sqrt{i d \left(c x - i\right)} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(-I*f*(c*x + I))**(3/2)*(a + b*asinh(c*x))**2, x)","F",0
579,0,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(1/2),x)","\int \frac{\left(- i f \left(c x + i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{i d \left(c x - i\right)}}\, dx"," ",0,"Integral((-I*f*(c*x + I))**(3/2)*(a + b*asinh(c*x))**2/sqrt(I*d*(c*x - I)), x)","F",0
580,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(3/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((f-I*c*f*x)**(5/2)*(a+b*asinh(c*x))**2/(d+I*c*d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,0,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(1/2),x)","\int \frac{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((I*d*(c*x - I))**(3/2)*(a + b*asinh(c*x))**2/sqrt(-I*f*(c*x + I)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{\sqrt{i d \left(c x - i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(a + b*asinh(c*x))**2/sqrt(-I*f*(c*x + I)), x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{i d \left(c x - i\right)} \sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(sqrt(I*d*(c*x - I))*sqrt(-I*f*(c*x + I))), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \sqrt{- i f \left(c x + i\right)}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/((I*d*(c*x - I))**(3/2)*sqrt(-I*f*(c*x + I))), x)","F",0
593,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(3/2),x)","\int \frac{\sqrt{i d \left(c x - i\right)} \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(I*d*(c*x - I))*(a + b*asinh(c*x))**2/(-I*f*(c*x + I))**(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(f-I*c*f*x)**(3/2)/(d+I*c*d*x)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{i d \left(c x - i\right)} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(sqrt(I*d*(c*x - I))*(-I*f*(c*x + I))**(3/2)), x)","F",0
598,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(i d \left(c x - i\right)\right)^{\frac{3}{2}} \left(- i f \left(c x + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/((I*d*(c*x - I))**(3/2)*(-I*f*(c*x + I))**(3/2)), x)","F",0
599,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(5/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**(3/2)*(a+b*asinh(c*x))**2/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(d+I*c*d*x)**(1/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(f-I*c*f*x)**(5/2)/(d+I*c*d*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(3/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(d+I*c*d*x)**(5/2)/(f-I*c*f*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,1,593,0,18.002678," ","integrate((e*x**2+d)**4*(a+b*asinh(c*x)),x)","\begin{cases} a d^{4} x + \frac{4 a d^{3} e x^{3}}{3} + \frac{6 a d^{2} e^{2} x^{5}}{5} + \frac{4 a d e^{3} x^{7}}{7} + \frac{a e^{4} x^{9}}{9} + b d^{4} x \operatorname{asinh}{\left(c x \right)} + \frac{4 b d^{3} e x^{3} \operatorname{asinh}{\left(c x \right)}}{3} + \frac{6 b d^{2} e^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} + \frac{4 b d e^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} + \frac{b e^{4} x^{9} \operatorname{asinh}{\left(c x \right)}}{9} - \frac{b d^{4} \sqrt{c^{2} x^{2} + 1}}{c} - \frac{4 b d^{3} e x^{2} \sqrt{c^{2} x^{2} + 1}}{9 c} - \frac{6 b d^{2} e^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25 c} - \frac{4 b d e^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{49 c} - \frac{b e^{4} x^{8} \sqrt{c^{2} x^{2} + 1}}{81 c} + \frac{8 b d^{3} e \sqrt{c^{2} x^{2} + 1}}{9 c^{3}} + \frac{8 b d^{2} e^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{3}} + \frac{24 b d e^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{245 c^{3}} + \frac{8 b e^{4} x^{6} \sqrt{c^{2} x^{2} + 1}}{567 c^{3}} - \frac{16 b d^{2} e^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{5}} - \frac{32 b d e^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{245 c^{5}} - \frac{16 b e^{4} x^{4} \sqrt{c^{2} x^{2} + 1}}{945 c^{5}} + \frac{64 b d e^{3} \sqrt{c^{2} x^{2} + 1}}{245 c^{7}} + \frac{64 b e^{4} x^{2} \sqrt{c^{2} x^{2} + 1}}{2835 c^{7}} - \frac{128 b e^{4} \sqrt{c^{2} x^{2} + 1}}{2835 c^{9}} & \text{for}\: c \neq 0 \\a \left(d^{4} x + \frac{4 d^{3} e x^{3}}{3} + \frac{6 d^{2} e^{2} x^{5}}{5} + \frac{4 d e^{3} x^{7}}{7} + \frac{e^{4} x^{9}}{9}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**4*x + 4*a*d**3*e*x**3/3 + 6*a*d**2*e**2*x**5/5 + 4*a*d*e**3*x**7/7 + a*e**4*x**9/9 + b*d**4*x*asinh(c*x) + 4*b*d**3*e*x**3*asinh(c*x)/3 + 6*b*d**2*e**2*x**5*asinh(c*x)/5 + 4*b*d*e**3*x**7*asinh(c*x)/7 + b*e**4*x**9*asinh(c*x)/9 - b*d**4*sqrt(c**2*x**2 + 1)/c - 4*b*d**3*e*x**2*sqrt(c**2*x**2 + 1)/(9*c) - 6*b*d**2*e**2*x**4*sqrt(c**2*x**2 + 1)/(25*c) - 4*b*d*e**3*x**6*sqrt(c**2*x**2 + 1)/(49*c) - b*e**4*x**8*sqrt(c**2*x**2 + 1)/(81*c) + 8*b*d**3*e*sqrt(c**2*x**2 + 1)/(9*c**3) + 8*b*d**2*e**2*x**2*sqrt(c**2*x**2 + 1)/(25*c**3) + 24*b*d*e**3*x**4*sqrt(c**2*x**2 + 1)/(245*c**3) + 8*b*e**4*x**6*sqrt(c**2*x**2 + 1)/(567*c**3) - 16*b*d**2*e**2*sqrt(c**2*x**2 + 1)/(25*c**5) - 32*b*d*e**3*x**2*sqrt(c**2*x**2 + 1)/(245*c**5) - 16*b*e**4*x**4*sqrt(c**2*x**2 + 1)/(945*c**5) + 64*b*d*e**3*sqrt(c**2*x**2 + 1)/(245*c**7) + 64*b*e**4*x**2*sqrt(c**2*x**2 + 1)/(2835*c**7) - 128*b*e**4*sqrt(c**2*x**2 + 1)/(2835*c**9), Ne(c, 0)), (a*(d**4*x + 4*d**3*e*x**3/3 + 6*d**2*e**2*x**5/5 + 4*d*e**3*x**7/7 + e**4*x**9/9), True))","A",0
607,1,389,0,6.648755," ","integrate((e*x**2+d)**3*(a+b*asinh(c*x)),x)","\begin{cases} a d^{3} x + a d^{2} e x^{3} + \frac{3 a d e^{2} x^{5}}{5} + \frac{a e^{3} x^{7}}{7} + b d^{3} x \operatorname{asinh}{\left(c x \right)} + b d^{2} e x^{3} \operatorname{asinh}{\left(c x \right)} + \frac{3 b d e^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} + \frac{b e^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{b d^{3} \sqrt{c^{2} x^{2} + 1}}{c} - \frac{b d^{2} e x^{2} \sqrt{c^{2} x^{2} + 1}}{3 c} - \frac{3 b d e^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25 c} - \frac{b e^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{49 c} + \frac{2 b d^{2} e \sqrt{c^{2} x^{2} + 1}}{3 c^{3}} + \frac{4 b d e^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{3}} + \frac{6 b e^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{245 c^{3}} - \frac{8 b d e^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{5}} - \frac{8 b e^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{245 c^{5}} + \frac{16 b e^{3} \sqrt{c^{2} x^{2} + 1}}{245 c^{7}} & \text{for}\: c \neq 0 \\a \left(d^{3} x + d^{2} e x^{3} + \frac{3 d e^{2} x^{5}}{5} + \frac{e^{3} x^{7}}{7}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + a*d**2*e*x**3 + 3*a*d*e**2*x**5/5 + a*e**3*x**7/7 + b*d**3*x*asinh(c*x) + b*d**2*e*x**3*asinh(c*x) + 3*b*d*e**2*x**5*asinh(c*x)/5 + b*e**3*x**7*asinh(c*x)/7 - b*d**3*sqrt(c**2*x**2 + 1)/c - b*d**2*e*x**2*sqrt(c**2*x**2 + 1)/(3*c) - 3*b*d*e**2*x**4*sqrt(c**2*x**2 + 1)/(25*c) - b*e**3*x**6*sqrt(c**2*x**2 + 1)/(49*c) + 2*b*d**2*e*sqrt(c**2*x**2 + 1)/(3*c**3) + 4*b*d*e**2*x**2*sqrt(c**2*x**2 + 1)/(25*c**3) + 6*b*e**3*x**4*sqrt(c**2*x**2 + 1)/(245*c**3) - 8*b*d*e**2*sqrt(c**2*x**2 + 1)/(25*c**5) - 8*b*e**3*x**2*sqrt(c**2*x**2 + 1)/(245*c**5) + 16*b*e**3*sqrt(c**2*x**2 + 1)/(245*c**7), Ne(c, 0)), (a*(d**3*x + d**2*e*x**3 + 3*d*e**2*x**5/5 + e**3*x**7/7), True))","A",0
608,1,240,0,2.317751," ","integrate((e*x**2+d)**2*(a+b*asinh(c*x)),x)","\begin{cases} a d^{2} x + \frac{2 a d e x^{3}}{3} + \frac{a e^{2} x^{5}}{5} + b d^{2} x \operatorname{asinh}{\left(c x \right)} + \frac{2 b d e x^{3} \operatorname{asinh}{\left(c x \right)}}{3} + \frac{b e^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{b d^{2} \sqrt{c^{2} x^{2} + 1}}{c} - \frac{2 b d e x^{2} \sqrt{c^{2} x^{2} + 1}}{9 c} - \frac{b e^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25 c} + \frac{4 b d e \sqrt{c^{2} x^{2} + 1}}{9 c^{3}} + \frac{4 b e^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{75 c^{3}} - \frac{8 b e^{2} \sqrt{c^{2} x^{2} + 1}}{75 c^{5}} & \text{for}\: c \neq 0 \\a \left(d^{2} x + \frac{2 d e x^{3}}{3} + \frac{e^{2} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x + 2*a*d*e*x**3/3 + a*e**2*x**5/5 + b*d**2*x*asinh(c*x) + 2*b*d*e*x**3*asinh(c*x)/3 + b*e**2*x**5*asinh(c*x)/5 - b*d**2*sqrt(c**2*x**2 + 1)/c - 2*b*d*e*x**2*sqrt(c**2*x**2 + 1)/(9*c) - b*e**2*x**4*sqrt(c**2*x**2 + 1)/(25*c) + 4*b*d*e*sqrt(c**2*x**2 + 1)/(9*c**3) + 4*b*e**2*x**2*sqrt(c**2*x**2 + 1)/(75*c**3) - 8*b*e**2*sqrt(c**2*x**2 + 1)/(75*c**5), Ne(c, 0)), (a*(d**2*x + 2*d*e*x**3/3 + e**2*x**5/5), True))","A",0
609,1,109,0,0.556171," ","integrate((e*x**2+d)*(a+b*asinh(c*x)),x)","\begin{cases} a d x + \frac{a e x^{3}}{3} + b d x \operatorname{asinh}{\left(c x \right)} + \frac{b e x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{b d \sqrt{c^{2} x^{2} + 1}}{c} - \frac{b e x^{2} \sqrt{c^{2} x^{2} + 1}}{9 c} + \frac{2 b e \sqrt{c^{2} x^{2} + 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\a \left(d x + \frac{e x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**3/3 + b*d*x*asinh(c*x) + b*e*x**3*asinh(c*x)/3 - b*d*sqrt(c**2*x**2 + 1)/c - b*e*x**2*sqrt(c**2*x**2 + 1)/(9*c) + 2*b*e*sqrt(c**2*x**2 + 1)/(9*c**3), Ne(c, 0)), (a*(d*x + e*x**3/3), True))","A",0
610,1,26,0,0.140244," ","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
611,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x**2), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d)**2,x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x**2)**2, x)","F",0
613,1,989,0,13.828480," ","integrate((e*x**2+d)**3*(a+b*asinh(c*x))**2,x)","\begin{cases} a^{2} d^{3} x + a^{2} d^{2} e x^{3} + \frac{3 a^{2} d e^{2} x^{5}}{5} + \frac{a^{2} e^{3} x^{7}}{7} + 2 a b d^{3} x \operatorname{asinh}{\left(c x \right)} + 2 a b d^{2} e x^{3} \operatorname{asinh}{\left(c x \right)} + \frac{6 a b d e^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} + \frac{2 a b e^{3} x^{7} \operatorname{asinh}{\left(c x \right)}}{7} - \frac{2 a b d^{3} \sqrt{c^{2} x^{2} + 1}}{c} - \frac{2 a b d^{2} e x^{2} \sqrt{c^{2} x^{2} + 1}}{3 c} - \frac{6 a b d e^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25 c} - \frac{2 a b e^{3} x^{6} \sqrt{c^{2} x^{2} + 1}}{49 c} + \frac{4 a b d^{2} e \sqrt{c^{2} x^{2} + 1}}{3 c^{3}} + \frac{8 a b d e^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{3}} + \frac{12 a b e^{3} x^{4} \sqrt{c^{2} x^{2} + 1}}{245 c^{3}} - \frac{16 a b d e^{2} \sqrt{c^{2} x^{2} + 1}}{25 c^{5}} - \frac{16 a b e^{3} x^{2} \sqrt{c^{2} x^{2} + 1}}{245 c^{5}} + \frac{32 a b e^{3} \sqrt{c^{2} x^{2} + 1}}{245 c^{7}} + b^{2} d^{3} x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} d^{3} x + b^{2} d^{2} e x^{3} \operatorname{asinh}^{2}{\left(c x \right)} + \frac{2 b^{2} d^{2} e x^{3}}{9} + \frac{3 b^{2} d e^{2} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{6 b^{2} d e^{2} x^{5}}{125} + \frac{b^{2} e^{3} x^{7} \operatorname{asinh}^{2}{\left(c x \right)}}{7} + \frac{2 b^{2} e^{3} x^{7}}{343} - \frac{2 b^{2} d^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{c} - \frac{2 b^{2} d^{2} e x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c} - \frac{6 b^{2} d e^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25 c} - \frac{2 b^{2} e^{3} x^{6} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{49 c} - \frac{4 b^{2} d^{2} e x}{3 c^{2}} - \frac{8 b^{2} d e^{2} x^{3}}{75 c^{2}} - \frac{12 b^{2} e^{3} x^{5}}{1225 c^{2}} + \frac{4 b^{2} d^{2} e \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{3 c^{3}} + \frac{8 b^{2} d e^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25 c^{3}} + \frac{12 b^{2} e^{3} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{245 c^{3}} + \frac{16 b^{2} d e^{2} x}{25 c^{4}} + \frac{16 b^{2} e^{3} x^{3}}{735 c^{4}} - \frac{16 b^{2} d e^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25 c^{5}} - \frac{16 b^{2} e^{3} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{245 c^{5}} - \frac{32 b^{2} e^{3} x}{245 c^{6}} + \frac{32 b^{2} e^{3} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{245 c^{7}} & \text{for}\: c \neq 0 \\a^{2} \left(d^{3} x + d^{2} e x^{3} + \frac{3 d e^{2} x^{5}}{5} + \frac{e^{3} x^{7}}{7}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**3*x + a**2*d**2*e*x**3 + 3*a**2*d*e**2*x**5/5 + a**2*e**3*x**7/7 + 2*a*b*d**3*x*asinh(c*x) + 2*a*b*d**2*e*x**3*asinh(c*x) + 6*a*b*d*e**2*x**5*asinh(c*x)/5 + 2*a*b*e**3*x**7*asinh(c*x)/7 - 2*a*b*d**3*sqrt(c**2*x**2 + 1)/c - 2*a*b*d**2*e*x**2*sqrt(c**2*x**2 + 1)/(3*c) - 6*a*b*d*e**2*x**4*sqrt(c**2*x**2 + 1)/(25*c) - 2*a*b*e**3*x**6*sqrt(c**2*x**2 + 1)/(49*c) + 4*a*b*d**2*e*sqrt(c**2*x**2 + 1)/(3*c**3) + 8*a*b*d*e**2*x**2*sqrt(c**2*x**2 + 1)/(25*c**3) + 12*a*b*e**3*x**4*sqrt(c**2*x**2 + 1)/(245*c**3) - 16*a*b*d*e**2*sqrt(c**2*x**2 + 1)/(25*c**5) - 16*a*b*e**3*x**2*sqrt(c**2*x**2 + 1)/(245*c**5) + 32*a*b*e**3*sqrt(c**2*x**2 + 1)/(245*c**7) + b**2*d**3*x*asinh(c*x)**2 + 2*b**2*d**3*x + b**2*d**2*e*x**3*asinh(c*x)**2 + 2*b**2*d**2*e*x**3/9 + 3*b**2*d*e**2*x**5*asinh(c*x)**2/5 + 6*b**2*d*e**2*x**5/125 + b**2*e**3*x**7*asinh(c*x)**2/7 + 2*b**2*e**3*x**7/343 - 2*b**2*d**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - 2*b**2*d**2*e*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c) - 6*b**2*d*e**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(25*c) - 2*b**2*e**3*x**6*sqrt(c**2*x**2 + 1)*asinh(c*x)/(49*c) - 4*b**2*d**2*e*x/(3*c**2) - 8*b**2*d*e**2*x**3/(75*c**2) - 12*b**2*e**3*x**5/(1225*c**2) + 4*b**2*d**2*e*sqrt(c**2*x**2 + 1)*asinh(c*x)/(3*c**3) + 8*b**2*d*e**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(25*c**3) + 12*b**2*e**3*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(245*c**3) + 16*b**2*d*e**2*x/(25*c**4) + 16*b**2*e**3*x**3/(735*c**4) - 16*b**2*d*e**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(25*c**5) - 16*b**2*e**3*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(245*c**5) - 32*b**2*e**3*x/(245*c**6) + 32*b**2*e**3*sqrt(c**2*x**2 + 1)*asinh(c*x)/(245*c**7), Ne(c, 0)), (a**2*(d**3*x + d**2*e*x**3 + 3*d*e**2*x**5/5 + e**3*x**7/7), True))","A",0
614,1,595,0,4.918591," ","integrate((e*x**2+d)**2*(a+b*asinh(c*x))**2,x)","\begin{cases} a^{2} d^{2} x + \frac{2 a^{2} d e x^{3}}{3} + \frac{a^{2} e^{2} x^{5}}{5} + 2 a b d^{2} x \operatorname{asinh}{\left(c x \right)} + \frac{4 a b d e x^{3} \operatorname{asinh}{\left(c x \right)}}{3} + \frac{2 a b e^{2} x^{5} \operatorname{asinh}{\left(c x \right)}}{5} - \frac{2 a b d^{2} \sqrt{c^{2} x^{2} + 1}}{c} - \frac{4 a b d e x^{2} \sqrt{c^{2} x^{2} + 1}}{9 c} - \frac{2 a b e^{2} x^{4} \sqrt{c^{2} x^{2} + 1}}{25 c} + \frac{8 a b d e \sqrt{c^{2} x^{2} + 1}}{9 c^{3}} + \frac{8 a b e^{2} x^{2} \sqrt{c^{2} x^{2} + 1}}{75 c^{3}} - \frac{16 a b e^{2} \sqrt{c^{2} x^{2} + 1}}{75 c^{5}} + b^{2} d^{2} x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} d^{2} x + \frac{2 b^{2} d e x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{4 b^{2} d e x^{3}}{27} + \frac{b^{2} e^{2} x^{5} \operatorname{asinh}^{2}{\left(c x \right)}}{5} + \frac{2 b^{2} e^{2} x^{5}}{125} - \frac{2 b^{2} d^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{c} - \frac{4 b^{2} d e x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c} - \frac{2 b^{2} e^{2} x^{4} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{25 c} - \frac{8 b^{2} d e x}{9 c^{2}} - \frac{8 b^{2} e^{2} x^{3}}{225 c^{2}} + \frac{8 b^{2} d e \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c^{3}} + \frac{8 b^{2} e^{2} x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{75 c^{3}} + \frac{16 b^{2} e^{2} x}{75 c^{4}} - \frac{16 b^{2} e^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{75 c^{5}} & \text{for}\: c \neq 0 \\a^{2} \left(d^{2} x + \frac{2 d e x^{3}}{3} + \frac{e^{2} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x + 2*a**2*d*e*x**3/3 + a**2*e**2*x**5/5 + 2*a*b*d**2*x*asinh(c*x) + 4*a*b*d*e*x**3*asinh(c*x)/3 + 2*a*b*e**2*x**5*asinh(c*x)/5 - 2*a*b*d**2*sqrt(c**2*x**2 + 1)/c - 4*a*b*d*e*x**2*sqrt(c**2*x**2 + 1)/(9*c) - 2*a*b*e**2*x**4*sqrt(c**2*x**2 + 1)/(25*c) + 8*a*b*d*e*sqrt(c**2*x**2 + 1)/(9*c**3) + 8*a*b*e**2*x**2*sqrt(c**2*x**2 + 1)/(75*c**3) - 16*a*b*e**2*sqrt(c**2*x**2 + 1)/(75*c**5) + b**2*d**2*x*asinh(c*x)**2 + 2*b**2*d**2*x + 2*b**2*d*e*x**3*asinh(c*x)**2/3 + 4*b**2*d*e*x**3/27 + b**2*e**2*x**5*asinh(c*x)**2/5 + 2*b**2*e**2*x**5/125 - 2*b**2*d**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - 4*b**2*d*e*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c) - 2*b**2*e**2*x**4*sqrt(c**2*x**2 + 1)*asinh(c*x)/(25*c) - 8*b**2*d*e*x/(9*c**2) - 8*b**2*e**2*x**3/(225*c**2) + 8*b**2*d*e*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c**3) + 8*b**2*e**2*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(75*c**3) + 16*b**2*e**2*x/(75*c**4) - 16*b**2*e**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(75*c**5), Ne(c, 0)), (a**2*(d**2*x + 2*d*e*x**3/3 + e**2*x**5/5), True))","A",0
615,1,279,0,1.372937," ","integrate((e*x**2+d)*(a+b*asinh(c*x))**2,x)","\begin{cases} a^{2} d x + \frac{a^{2} e x^{3}}{3} + 2 a b d x \operatorname{asinh}{\left(c x \right)} + \frac{2 a b e x^{3} \operatorname{asinh}{\left(c x \right)}}{3} - \frac{2 a b d \sqrt{c^{2} x^{2} + 1}}{c} - \frac{2 a b e x^{2} \sqrt{c^{2} x^{2} + 1}}{9 c} + \frac{4 a b e \sqrt{c^{2} x^{2} + 1}}{9 c^{3}} + b^{2} d x \operatorname{asinh}^{2}{\left(c x \right)} + 2 b^{2} d x + \frac{b^{2} e x^{3} \operatorname{asinh}^{2}{\left(c x \right)}}{3} + \frac{2 b^{2} e x^{3}}{27} - \frac{2 b^{2} d \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{c} - \frac{2 b^{2} e x^{2} \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c} - \frac{4 b^{2} e x}{9 c^{2}} + \frac{4 b^{2} e \sqrt{c^{2} x^{2} + 1} \operatorname{asinh}{\left(c x \right)}}{9 c^{3}} & \text{for}\: c \neq 0 \\a^{2} \left(d x + \frac{e x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x + a**2*e*x**3/3 + 2*a*b*d*x*asinh(c*x) + 2*a*b*e*x**3*asinh(c*x)/3 - 2*a*b*d*sqrt(c**2*x**2 + 1)/c - 2*a*b*e*x**2*sqrt(c**2*x**2 + 1)/(9*c) + 4*a*b*e*sqrt(c**2*x**2 + 1)/(9*c**3) + b**2*d*x*asinh(c*x)**2 + 2*b**2*d*x + b**2*e*x**3*asinh(c*x)**2/3 + 2*b**2*e*x**3/27 - 2*b**2*d*sqrt(c**2*x**2 + 1)*asinh(c*x)/c - 2*b**2*e*x**2*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c) - 4*b**2*e*x/(9*c**2) + 4*b**2*e*sqrt(c**2*x**2 + 1)*asinh(c*x)/(9*c**3), Ne(c, 0)), (a**2*(d*x + e*x**3/3), True))","A",0
616,1,82,0,0.273331," ","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
617,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d + e*x**2), x)","F",0
618,0,0,0,0.000000," ","integrate((e*x**2+d)**3/(a+b*asinh(c*x)),x)","\int \frac{\left(d + e x^{2}\right)^{3}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x**2)**3/(a + b*asinh(c*x)), x)","F",0
619,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(a+b*asinh(c*x)),x)","\int \frac{\left(d + e x^{2}\right)^{2}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x**2)**2/(a + b*asinh(c*x)), x)","F",0
620,0,0,0,0.000000," ","integrate((e*x**2+d)/(a+b*asinh(c*x)),x)","\int \frac{d + e x^{2}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x**2)/(a + b*asinh(c*x)), x)","F",0
621,0,0,0,0.000000," ","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
622,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(d + e*x**2)), x)","F",0
623,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*asinh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(a+b*asinh(c*x))**2,x)","\int \frac{\left(d + e x^{2}\right)^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x**2)**2/(a + b*asinh(c*x))**2, x)","F",0
625,0,0,0,0.000000," ","integrate((e*x**2+d)/(a+b*asinh(c*x))**2,x)","\int \frac{d + e x^{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
626,0,0,0,0.000000," ","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
627,0,0,0,0.000000," ","integrate(1/(e*x**2+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^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(d + e*x**2)), x)","F",0
628,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*asinh(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*asinh(c*x))**(1/2),x)","\int \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \left(d + e x^{2}\right)^{2}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c*x))*(d + e*x**2)**2, x)","F",0
630,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*asinh(c*x))**(1/2),x)","\int \sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \left(d + e x^{2}\right)\, dx"," ",0,"Integral(sqrt(a + b*asinh(c*x))*(d + e*x**2), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(1/2),x)","\int \sqrt{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c*x)), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(1/2)/(e*x**2+d),x)","\int \frac{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}}}{d + e x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c*x))/(d + e*x**2), x)","F",0
633,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(1/2)/(e*x**2+d)**2,x)","\int \frac{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}}}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*asinh(c*x))/(d + e*x**2)**2, x)","F",0
634,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*asinh(c*x))**(3/2),x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}} \left(d + e x^{2}\right)\, dx"," ",0,"Integral((a + b*asinh(c*x))**(3/2)*(d + e*x**2), x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(3/2),x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**(3/2), x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(3/2)/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**(3/2)/(d + e*x**2), x)","F",0
637,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**(3/2)/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(a+b*asinh(c*x))**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}}}\, dx"," ",0,"Integral((d + e*x**2)**2/sqrt(a + b*asinh(c*x)), x)","F",0
639,0,0,0,0.000000," ","integrate((e*x**2+d)/(a+b*asinh(c*x))**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt(a + b*asinh(c*x)), x)","F",0
640,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asinh(c*x)), x)","F",0
641,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(a+b*asinh(c*x))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*asinh(c*x))*(d + e*x**2)), x)","F",0
642,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*asinh(c*x))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asinh}{\left(c x \right)}} \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + b*asinh(c*x))*(d + e*x**2)**2), x)","F",0
643,0,0,0,0.000000," ","integrate((e*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","\int \frac{d + e x^{2}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x**2)/(a + b*asinh(c*x))**(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**(-3/2), x)","F",0
645,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(a+b*asinh(c*x))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{\frac{3}{2}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**(3/2)*(d + e*x**2)), x)","F",0
646,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*asinh(c*x))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))*(e*x**2+d)**(1/2),x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))*sqrt(d + e*x**2), x)","F",0
648,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/sqrt(d + e*x**2), x)","F",0
649,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x**2)**(3/2), x)","F",0
650,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asinh}{\left(c x \right)}}{\left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))/(d + e*x**2)**(5/2), x)","F",0
651,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))/(e*x**2+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2*(e*x**2+d)**(1/2),x)","\int \left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2*sqrt(d + e*x**2), x)","F",0
653,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/sqrt(d + e*x**2), x)","F",0
654,0,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asinh(c*x))**2/(d + e*x**2)**(3/2), x)","F",0
655,-1,0,0,0.000000," ","integrate((a+b*asinh(c*x))**2/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)/(a+b*asinh(c*x)),x)","\int \frac{\sqrt{d + e x^{2}}}{a + b \operatorname{asinh}{\left(c x \right)}}\, dx"," ",0,"Integral(sqrt(d + e*x**2)/(a + b*asinh(c*x)), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*sqrt(d + e*x**2)), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(3/2)/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(d + e*x**2)**(3/2)), x)","F",0
659,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(5/2)/(a+b*asinh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))*(d + e*x**2)**(5/2)), x)","F",0
660,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)/(a+b*asinh(c*x))**2,x)","\int \frac{\sqrt{d + e x^{2}}}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x**2)/(a + b*asinh(c*x))**2, x)","F",0
661,0,0,0,0.000000," ","integrate(1/(a+b*asinh(c*x))**2/(e*x**2+d)**(1/2),x)","\int \frac{1}{\left(a + b \operatorname{asinh}{\left(c x \right)}\right)^{2} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*sqrt(d + e*x**2)), x)","F",0
662,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(3/2)/(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^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(d + e*x**2)**(3/2)), x)","F",0
663,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(5/2)/(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^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*asinh(c*x))**2*(d + e*x**2)**(5/2)), x)","F",0
