1,1,258,0,1.276738," ","integrate((e*x+d)**3*acosh(c*x),x)","\begin{cases} d^{3} x \operatorname{acosh}{\left(c x \right)} + \frac{3 d^{2} e x^{2} \operatorname{acosh}{\left(c x \right)}}{2} + d e^{2} x^{3} \operatorname{acosh}{\left(c x \right)} + \frac{e^{3} x^{4} \operatorname{acosh}{\left(c x \right)}}{4} - \frac{d^{3} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{3 d^{2} e x \sqrt{c^{2} x^{2} - 1}}{4 c} - \frac{d e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} - \frac{e^{3} x^{3} \sqrt{c^{2} x^{2} - 1}}{16 c} - \frac{3 d^{2} e \operatorname{acosh}{\left(c x \right)}}{4 c^{2}} - \frac{2 d e^{2} \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} - \frac{3 e^{3} x \sqrt{c^{2} x^{2} - 1}}{32 c^{3}} - \frac{3 e^{3} \operatorname{acosh}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\\frac{i \pi \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*x*acosh(c*x) + 3*d**2*e*x**2*acosh(c*x)/2 + d*e**2*x**3*acosh(c*x) + e**3*x**4*acosh(c*x)/4 - d**3*sqrt(c**2*x**2 - 1)/c - 3*d**2*e*x*sqrt(c**2*x**2 - 1)/(4*c) - d*e**2*x**2*sqrt(c**2*x**2 - 1)/(3*c) - e**3*x**3*sqrt(c**2*x**2 - 1)/(16*c) - 3*d**2*e*acosh(c*x)/(4*c**2) - 2*d*e**2*sqrt(c**2*x**2 - 1)/(3*c**3) - 3*e**3*x*sqrt(c**2*x**2 - 1)/(32*c**3) - 3*e**3*acosh(c*x)/(32*c**4), Ne(c, 0)), (I*pi*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)/2, True))","A",0
2,1,155,0,0.575357," ","integrate((e*x+d)**2*acosh(c*x),x)","\begin{cases} d^{2} x \operatorname{acosh}{\left(c x \right)} + d e x^{2} \operatorname{acosh}{\left(c x \right)} + \frac{e^{2} x^{3} \operatorname{acosh}{\left(c x \right)}}{3} - \frac{d^{2} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{d e x \sqrt{c^{2} x^{2} - 1}}{2 c} - \frac{e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{9 c} - \frac{d e \operatorname{acosh}{\left(c x \right)}}{2 c^{2}} - \frac{2 e^{2} \sqrt{c^{2} x^{2} - 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\\frac{i \pi \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*x*acosh(c*x) + d*e*x**2*acosh(c*x) + e**2*x**3*acosh(c*x)/3 - d**2*sqrt(c**2*x**2 - 1)/c - d*e*x*sqrt(c**2*x**2 - 1)/(2*c) - e**2*x**2*sqrt(c**2*x**2 - 1)/(9*c) - d*e*acosh(c*x)/(2*c**2) - 2*e**2*sqrt(c**2*x**2 - 1)/(9*c**3), Ne(c, 0)), (I*pi*(d**2*x + d*e*x**2 + e**2*x**3/3)/2, True))","A",0
3,1,80,0,0.260997," ","integrate((e*x+d)*acosh(c*x),x)","\begin{cases} d x \operatorname{acosh}{\left(c x \right)} + \frac{e x^{2} \operatorname{acosh}{\left(c x \right)}}{2} - \frac{d \sqrt{c^{2} x^{2} - 1}}{c} - \frac{e x \sqrt{c^{2} x^{2} - 1}}{4 c} - \frac{e \operatorname{acosh}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\frac{i \pi \left(d x + \frac{e x^{2}}{2}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*x*acosh(c*x) + e*x**2*acosh(c*x)/2 - d*sqrt(c**2*x**2 - 1)/c - e*x*sqrt(c**2*x**2 - 1)/(4*c) - e*acosh(c*x)/(4*c**2), Ne(c, 0)), (I*pi*(d*x + e*x**2/2)/2, True))","A",0
4,0,0,0,0.000000," ","integrate(acosh(c*x)/(e*x+d),x)","\int \frac{\operatorname{acosh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral(acosh(c*x)/(d + e*x), x)","F",0
5,0,0,0,0.000000," ","integrate(acosh(c*x)/(e*x+d)**2,x)","\int \frac{\operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(acosh(c*x)/(d + e*x)**2, x)","F",0
6,0,0,0,0.000000," ","integrate(acosh(c*x)/(e*x+d)**3,x)","\int \frac{\operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(acosh(c*x)/(d + e*x)**3, x)","F",0
7,0,0,0,0.000000," ","integrate(acosh(c*x)/(e*x+d)**4,x)","\int \frac{\operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(acosh(c*x)/(d + e*x)**4, x)","F",0
8,1,371,0,2.457756," ","integrate((e*x+d)**3*acosh(c*x)**2,x)","\begin{cases} d^{3} x \operatorname{acosh}^{2}{\left(c x \right)} + 2 d^{3} x + \frac{3 d^{2} e x^{2} \operatorname{acosh}^{2}{\left(c x \right)}}{2} + \frac{3 d^{2} e x^{2}}{4} + d e^{2} x^{3} \operatorname{acosh}^{2}{\left(c x \right)} + \frac{2 d e^{2} x^{3}}{9} + \frac{e^{3} x^{4} \operatorname{acosh}^{2}{\left(c x \right)}}{4} + \frac{e^{3} x^{4}}{32} - \frac{2 d^{3} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{3 d^{2} e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{2 c} - \frac{2 d e^{2} x^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{3 c} - \frac{e^{3} x^{3} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{8 c} - \frac{3 d^{2} e \operatorname{acosh}^{2}{\left(c x \right)}}{4 c^{2}} + \frac{4 d e^{2} x}{3 c^{2}} + \frac{3 e^{3} x^{2}}{32 c^{2}} - \frac{4 d e^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{3 c^{3}} - \frac{3 e^{3} x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{16 c^{3}} - \frac{3 e^{3} \operatorname{acosh}^{2}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\- \frac{\pi^{2} \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right)}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*x*acosh(c*x)**2 + 2*d**3*x + 3*d**2*e*x**2*acosh(c*x)**2/2 + 3*d**2*e*x**2/4 + d*e**2*x**3*acosh(c*x)**2 + 2*d*e**2*x**3/9 + e**3*x**4*acosh(c*x)**2/4 + e**3*x**4/32 - 2*d**3*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - 3*d**2*e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(2*c) - 2*d*e**2*x**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(3*c) - e**3*x**3*sqrt(c**2*x**2 - 1)*acosh(c*x)/(8*c) - 3*d**2*e*acosh(c*x)**2/(4*c**2) + 4*d*e**2*x/(3*c**2) + 3*e**3*x**2/(32*c**2) - 4*d*e**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(3*c**3) - 3*e**3*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(16*c**3) - 3*e**3*acosh(c*x)**2/(32*c**4), Ne(c, 0)), (-pi**2*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)/4, True))","A",0
9,1,223,0,1.209556," ","integrate((e*x+d)**2*acosh(c*x)**2,x)","\begin{cases} d^{2} x \operatorname{acosh}^{2}{\left(c x \right)} + 2 d^{2} x + d e x^{2} \operatorname{acosh}^{2}{\left(c x \right)} + \frac{d e x^{2}}{2} + \frac{e^{2} x^{3} \operatorname{acosh}^{2}{\left(c x \right)}}{3} + \frac{2 e^{2} x^{3}}{27} - \frac{2 d^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{d e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{2 e^{2} x^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{9 c} - \frac{d e \operatorname{acosh}^{2}{\left(c x \right)}}{2 c^{2}} + \frac{4 e^{2} x}{9 c^{2}} - \frac{4 e^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{9 c^{3}} & \text{for}\: c \neq 0 \\- \frac{\pi^{2} \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right)}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*x*acosh(c*x)**2 + 2*d**2*x + d*e*x**2*acosh(c*x)**2 + d*e*x**2/2 + e**2*x**3*acosh(c*x)**2/3 + 2*e**2*x**3/27 - 2*d**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - d*e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - 2*e**2*x**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(9*c) - d*e*acosh(c*x)**2/(2*c**2) + 4*e**2*x/(9*c**2) - 4*e**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(9*c**3), Ne(c, 0)), (-pi**2*(d**2*x + d*e*x**2 + e**2*x**3/3)/4, True))","A",0
10,1,110,0,0.529022," ","integrate((e*x+d)*acosh(c*x)**2,x)","\begin{cases} d x \operatorname{acosh}^{2}{\left(c x \right)} + 2 d x + \frac{e x^{2} \operatorname{acosh}^{2}{\left(c x \right)}}{2} + \frac{e x^{2}}{4} - \frac{2 d \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{2 c} - \frac{e \operatorname{acosh}^{2}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\- \frac{\pi^{2} \left(d x + \frac{e x^{2}}{2}\right)}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*x*acosh(c*x)**2 + 2*d*x + e*x**2*acosh(c*x)**2/2 + e*x**2/4 - 2*d*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(2*c) - e*acosh(c*x)**2/(4*c**2), Ne(c, 0)), (-pi**2*(d*x + e*x**2/2)/4, True))","A",0
11,0,0,0,0.000000," ","integrate(acosh(c*x)**2/(e*x+d),x)","\int \frac{\operatorname{acosh}^{2}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral(acosh(c*x)**2/(d + e*x), x)","F",0
12,0,0,0,0.000000," ","integrate(acosh(c*x)**2/(e*x+d)**2,x)","\int \frac{\operatorname{acosh}^{2}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(acosh(c*x)**2/(d + e*x)**2, x)","F",0
13,0,0,0,0.000000," ","integrate(acosh(c*x)**2/(e*x+d)**3,x)","\int \frac{\operatorname{acosh}^{2}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(acosh(c*x)**2/(d + e*x)**3, x)","F",0
14,1,323,0,1.525429," ","integrate((e*x+d)**3*(a+b*acosh(c*x)),x)","\begin{cases} a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + b d^{3} x \operatorname{acosh}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{acosh}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{acosh}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{acosh}{\left(c x \right)}}{4} - \frac{b d^{3} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{3 b d^{2} e x \sqrt{c^{2} x^{2} - 1}}{4 c} - \frac{b d e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} - \frac{b e^{3} x^{3} \sqrt{c^{2} x^{2} - 1}}{16 c} - \frac{3 b d^{2} e \operatorname{acosh}{\left(c x \right)}}{4 c^{2}} - \frac{2 b d e^{2} \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} - \frac{3 b e^{3} x \sqrt{c^{2} x^{2} - 1}}{32 c^{3}} - \frac{3 b e^{3} \operatorname{acosh}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right) \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*d**3*x*acosh(c*x) + 3*b*d**2*e*x**2*acosh(c*x)/2 + b*d*e**2*x**3*acosh(c*x) + b*e**3*x**4*acosh(c*x)/4 - b*d**3*sqrt(c**2*x**2 - 1)/c - 3*b*d**2*e*x*sqrt(c**2*x**2 - 1)/(4*c) - b*d*e**2*x**2*sqrt(c**2*x**2 - 1)/(3*c) - b*e**3*x**3*sqrt(c**2*x**2 - 1)/(16*c) - 3*b*d**2*e*acosh(c*x)/(4*c**2) - 2*b*d*e**2*sqrt(c**2*x**2 - 1)/(3*c**3) - 3*b*e**3*x*sqrt(c**2*x**2 - 1)/(32*c**3) - 3*b*e**3*acosh(c*x)/(32*c**4), Ne(c, 0)), ((a + I*pi*b/2)*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
15,1,197,0,0.683250," ","integrate((e*x+d)**2*(a+b*acosh(c*x)),x)","\begin{cases} a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} x \operatorname{acosh}{\left(c x \right)} + b d e x^{2} \operatorname{acosh}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{acosh}{\left(c x \right)}}{3} - \frac{b d^{2} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{b d e x \sqrt{c^{2} x^{2} - 1}}{2 c} - \frac{b e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{9 c} - \frac{b d e \operatorname{acosh}{\left(c x \right)}}{2 c^{2}} - \frac{2 b e^{2} \sqrt{c^{2} x^{2} - 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right) \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + b*d**2*x*acosh(c*x) + b*d*e*x**2*acosh(c*x) + b*e**2*x**3*acosh(c*x)/3 - b*d**2*sqrt(c**2*x**2 - 1)/c - b*d*e*x*sqrt(c**2*x**2 - 1)/(2*c) - b*e**2*x**2*sqrt(c**2*x**2 - 1)/(9*c) - b*d*e*acosh(c*x)/(2*c**2) - 2*b*e**2*sqrt(c**2*x**2 - 1)/(9*c**3), Ne(c, 0)), ((a + I*pi*b/2)*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
16,1,105,0,0.341209," ","integrate((e*x+d)*(a+b*acosh(c*x)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + b d x \operatorname{acosh}{\left(c x \right)} + \frac{b e x^{2} \operatorname{acosh}{\left(c x \right)}}{2} - \frac{b d \sqrt{c^{2} x^{2} - 1}}{c} - \frac{b e x \sqrt{c^{2} x^{2} - 1}}{4 c} - \frac{b e \operatorname{acosh}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**2/2 + b*d*x*acosh(c*x) + b*e*x**2*acosh(c*x)/2 - b*d*sqrt(c**2*x**2 - 1)/c - b*e*x*sqrt(c**2*x**2 - 1)/(4*c) - b*e*acosh(c*x)/(4*c**2), Ne(c, 0)), ((a + I*pi*b/2)*(d*x + e*x**2/2), True))","A",0
17,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(d + e*x), x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(e*x+d)**2,x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(d + e*x)**2, x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(e*x+d)**3,x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(d + e*x)**3, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(e*x+d)**4,x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(d + e*x)**4, x)","F",0
21,1,750,0,3.701726," ","integrate((e*x+d)**3*(a+b*acosh(c*x))**2,x)","\begin{cases} a^{2} d^{3} x + \frac{3 a^{2} d^{2} e x^{2}}{2} + a^{2} d e^{2} x^{3} + \frac{a^{2} e^{3} x^{4}}{4} + 2 a b d^{3} x \operatorname{acosh}{\left(c x \right)} + 3 a b d^{2} e x^{2} \operatorname{acosh}{\left(c x \right)} + 2 a b d e^{2} x^{3} \operatorname{acosh}{\left(c x \right)} + \frac{a b e^{3} x^{4} \operatorname{acosh}{\left(c x \right)}}{2} - \frac{2 a b d^{3} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{3 a b d^{2} e x \sqrt{c^{2} x^{2} - 1}}{2 c} - \frac{2 a b d e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} - \frac{a b e^{3} x^{3} \sqrt{c^{2} x^{2} - 1}}{8 c} - \frac{3 a b d^{2} e \operatorname{acosh}{\left(c x \right)}}{2 c^{2}} - \frac{4 a b d e^{2} \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} - \frac{3 a b e^{3} x \sqrt{c^{2} x^{2} - 1}}{16 c^{3}} - \frac{3 a b e^{3} \operatorname{acosh}{\left(c x \right)}}{16 c^{4}} + b^{2} d^{3} x \operatorname{acosh}^{2}{\left(c x \right)} + 2 b^{2} d^{3} x + \frac{3 b^{2} d^{2} e x^{2} \operatorname{acosh}^{2}{\left(c x \right)}}{2} + \frac{3 b^{2} d^{2} e x^{2}}{4} + b^{2} d e^{2} x^{3} \operatorname{acosh}^{2}{\left(c x \right)} + \frac{2 b^{2} d e^{2} x^{3}}{9} + \frac{b^{2} e^{3} x^{4} \operatorname{acosh}^{2}{\left(c x \right)}}{4} + \frac{b^{2} e^{3} x^{4}}{32} - \frac{2 b^{2} d^{3} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{3 b^{2} d^{2} e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{2 c} - \frac{2 b^{2} d e^{2} x^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{3 c} - \frac{b^{2} e^{3} x^{3} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{8 c} - \frac{3 b^{2} d^{2} e \operatorname{acosh}^{2}{\left(c x \right)}}{4 c^{2}} + \frac{4 b^{2} d e^{2} x}{3 c^{2}} + \frac{3 b^{2} e^{3} x^{2}}{32 c^{2}} - \frac{4 b^{2} d e^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{3 c^{3}} - \frac{3 b^{2} e^{3} x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{16 c^{3}} - \frac{3 b^{2} e^{3} \operatorname{acosh}^{2}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right)^{2} \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**3*x + 3*a**2*d**2*e*x**2/2 + a**2*d*e**2*x**3 + a**2*e**3*x**4/4 + 2*a*b*d**3*x*acosh(c*x) + 3*a*b*d**2*e*x**2*acosh(c*x) + 2*a*b*d*e**2*x**3*acosh(c*x) + a*b*e**3*x**4*acosh(c*x)/2 - 2*a*b*d**3*sqrt(c**2*x**2 - 1)/c - 3*a*b*d**2*e*x*sqrt(c**2*x**2 - 1)/(2*c) - 2*a*b*d*e**2*x**2*sqrt(c**2*x**2 - 1)/(3*c) - a*b*e**3*x**3*sqrt(c**2*x**2 - 1)/(8*c) - 3*a*b*d**2*e*acosh(c*x)/(2*c**2) - 4*a*b*d*e**2*sqrt(c**2*x**2 - 1)/(3*c**3) - 3*a*b*e**3*x*sqrt(c**2*x**2 - 1)/(16*c**3) - 3*a*b*e**3*acosh(c*x)/(16*c**4) + b**2*d**3*x*acosh(c*x)**2 + 2*b**2*d**3*x + 3*b**2*d**2*e*x**2*acosh(c*x)**2/2 + 3*b**2*d**2*e*x**2/4 + b**2*d*e**2*x**3*acosh(c*x)**2 + 2*b**2*d*e**2*x**3/9 + b**2*e**3*x**4*acosh(c*x)**2/4 + b**2*e**3*x**4/32 - 2*b**2*d**3*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - 3*b**2*d**2*e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(2*c) - 2*b**2*d*e**2*x**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(3*c) - b**2*e**3*x**3*sqrt(c**2*x**2 - 1)*acosh(c*x)/(8*c) - 3*b**2*d**2*e*acosh(c*x)**2/(4*c**2) + 4*b**2*d*e**2*x/(3*c**2) + 3*b**2*e**3*x**2/(32*c**2) - 4*b**2*d*e**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(3*c**3) - 3*b**2*e**3*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(16*c**3) - 3*b**2*e**3*acosh(c*x)**2/(32*c**4), Ne(c, 0)), ((a + I*pi*b/2)**2*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
22,1,461,0,1.699972," ","integrate((e*x+d)**2*(a+b*acosh(c*x))**2,x)","\begin{cases} a^{2} d^{2} x + a^{2} d e x^{2} + \frac{a^{2} e^{2} x^{3}}{3} + 2 a b d^{2} x \operatorname{acosh}{\left(c x \right)} + 2 a b d e x^{2} \operatorname{acosh}{\left(c x \right)} + \frac{2 a b e^{2} x^{3} \operatorname{acosh}{\left(c x \right)}}{3} - \frac{2 a b d^{2} \sqrt{c^{2} x^{2} - 1}}{c} - \frac{a b d e x \sqrt{c^{2} x^{2} - 1}}{c} - \frac{2 a b e^{2} x^{2} \sqrt{c^{2} x^{2} - 1}}{9 c} - \frac{a b d e \operatorname{acosh}{\left(c x \right)}}{c^{2}} - \frac{4 a b e^{2} \sqrt{c^{2} x^{2} - 1}}{9 c^{3}} + b^{2} d^{2} x \operatorname{acosh}^{2}{\left(c x \right)} + 2 b^{2} d^{2} x + b^{2} d e x^{2} \operatorname{acosh}^{2}{\left(c x \right)} + \frac{b^{2} d e x^{2}}{2} + \frac{b^{2} e^{2} x^{3} \operatorname{acosh}^{2}{\left(c x \right)}}{3} + \frac{2 b^{2} e^{2} x^{3}}{27} - \frac{2 b^{2} d^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{b^{2} d e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{2 b^{2} e^{2} x^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{9 c} - \frac{b^{2} d e \operatorname{acosh}^{2}{\left(c x \right)}}{2 c^{2}} + \frac{4 b^{2} e^{2} x}{9 c^{2}} - \frac{4 b^{2} e^{2} \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{9 c^{3}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right)^{2} \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x + a**2*d*e*x**2 + a**2*e**2*x**3/3 + 2*a*b*d**2*x*acosh(c*x) + 2*a*b*d*e*x**2*acosh(c*x) + 2*a*b*e**2*x**3*acosh(c*x)/3 - 2*a*b*d**2*sqrt(c**2*x**2 - 1)/c - a*b*d*e*x*sqrt(c**2*x**2 - 1)/c - 2*a*b*e**2*x**2*sqrt(c**2*x**2 - 1)/(9*c) - a*b*d*e*acosh(c*x)/c**2 - 4*a*b*e**2*sqrt(c**2*x**2 - 1)/(9*c**3) + b**2*d**2*x*acosh(c*x)**2 + 2*b**2*d**2*x + b**2*d*e*x**2*acosh(c*x)**2 + b**2*d*e*x**2/2 + b**2*e**2*x**3*acosh(c*x)**2/3 + 2*b**2*e**2*x**3/27 - 2*b**2*d**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - b**2*d*e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - 2*b**2*e**2*x**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(9*c) - b**2*d*e*acosh(c*x)**2/(2*c**2) + 4*b**2*e**2*x/(9*c**2) - 4*b**2*e**2*sqrt(c**2*x**2 - 1)*acosh(c*x)/(9*c**3), Ne(c, 0)), ((a + I*pi*b/2)**2*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
23,1,240,0,0.705925," ","integrate((e*x+d)*(a+b*acosh(c*x))**2,x)","\begin{cases} a^{2} d x + \frac{a^{2} e x^{2}}{2} + 2 a b d x \operatorname{acosh}{\left(c x \right)} + a b e x^{2} \operatorname{acosh}{\left(c x \right)} - \frac{2 a b d \sqrt{c^{2} x^{2} - 1}}{c} - \frac{a b e x \sqrt{c^{2} x^{2} - 1}}{2 c} - \frac{a b e \operatorname{acosh}{\left(c x \right)}}{2 c^{2}} + b^{2} d x \operatorname{acosh}^{2}{\left(c x \right)} + 2 b^{2} d x + \frac{b^{2} e x^{2} \operatorname{acosh}^{2}{\left(c x \right)}}{2} + \frac{b^{2} e x^{2}}{4} - \frac{2 b^{2} d \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{c} - \frac{b^{2} e x \sqrt{c^{2} x^{2} - 1} \operatorname{acosh}{\left(c x \right)}}{2 c} - \frac{b^{2} e \operatorname{acosh}^{2}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\left(a + \frac{i \pi b}{2}\right)^{2} \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x + a**2*e*x**2/2 + 2*a*b*d*x*acosh(c*x) + a*b*e*x**2*acosh(c*x) - 2*a*b*d*sqrt(c**2*x**2 - 1)/c - a*b*e*x*sqrt(c**2*x**2 - 1)/(2*c) - a*b*e*acosh(c*x)/(2*c**2) + b**2*d*x*acosh(c*x)**2 + 2*b**2*d*x + b**2*e*x**2*acosh(c*x)**2/2 + b**2*e*x**2/4 - 2*b**2*d*sqrt(c**2*x**2 - 1)*acosh(c*x)/c - b**2*e*x*sqrt(c**2*x**2 - 1)*acosh(c*x)/(2*c) - b**2*e*acosh(c*x)**2/(4*c**2), Ne(c, 0)), ((a + I*pi*b/2)**2*(d*x + e*x**2/2), True))","A",0
24,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*acosh(c*x))**2/(d + e*x), x)","F",0
25,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**2/(d + e*x)**2, x)","F",0
26,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**2/(d + e*x)**3, x)","F",0
27,0,0,0,0.000000," ","integrate((e*x+d)**3/(a+b*acosh(c*x)),x)","\int \frac{\left(d + e x\right)^{3}}{a + b \operatorname{acosh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*acosh(c*x)), x)","F",0
28,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*acosh(c*x)),x)","\int \frac{\left(d + e x\right)^{2}}{a + b \operatorname{acosh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*acosh(c*x)), x)","F",0
29,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*acosh(c*x)),x)","\int \frac{d + e x}{a + b \operatorname{acosh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)/(a + b*acosh(c*x)), x)","F",0
30,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*acosh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*acosh(c*x))*(d + e*x)), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*acosh(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*acosh(c*x))*(d + e*x)**2), x)","F",0
32,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*acosh(c*x))**2,x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*acosh(c*x))**2, x)","F",0
33,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*acosh(c*x))**2,x)","\int \frac{d + e x}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)/(a + b*acosh(c*x))**2, x)","F",0
34,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*acosh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*acosh(c*x))**2*(d + e*x)), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*acosh(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*acosh(c*x))**2*(d + e*x)**2), x)","F",0
36,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*acosh(c*x))**3,x)","\int \left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{3} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*acosh(c*x))**3*(d + e*x)**m, x)","F",0
37,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*acosh(c*x))**2,x)","\int \left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*acosh(c*x))**2*(d + e*x)**m, x)","F",0
38,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*acosh(c*x)),x)","\int \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(d + e*x)**m, x)","F",0
39,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*acosh(c*x)),x)","\int \frac{\left(d + e x\right)^{m}}{a + b \operatorname{acosh}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*acosh(c*x)), x)","F",0
40,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*acosh(c*x))**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*acosh(c*x))**2, x)","F",0
41,1,503,0,16.256450," ","integrate((d*x**2+c)**4*acosh(a*x),x)","\begin{cases} c^{4} x \operatorname{acosh}{\left(a x \right)} + \frac{4 c^{3} d x^{3} \operatorname{acosh}{\left(a x \right)}}{3} + \frac{6 c^{2} d^{2} x^{5} \operatorname{acosh}{\left(a x \right)}}{5} + \frac{4 c d^{3} x^{7} \operatorname{acosh}{\left(a x \right)}}{7} + \frac{d^{4} x^{9} \operatorname{acosh}{\left(a x \right)}}{9} - \frac{c^{4} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{4 c^{3} d x^{2} \sqrt{a^{2} x^{2} - 1}}{9 a} - \frac{6 c^{2} d^{2} x^{4} \sqrt{a^{2} x^{2} - 1}}{25 a} - \frac{4 c d^{3} x^{6} \sqrt{a^{2} x^{2} - 1}}{49 a} - \frac{d^{4} x^{8} \sqrt{a^{2} x^{2} - 1}}{81 a} - \frac{8 c^{3} d \sqrt{a^{2} x^{2} - 1}}{9 a^{3}} - \frac{8 c^{2} d^{2} x^{2} \sqrt{a^{2} x^{2} - 1}}{25 a^{3}} - \frac{24 c d^{3} x^{4} \sqrt{a^{2} x^{2} - 1}}{245 a^{3}} - \frac{8 d^{4} x^{6} \sqrt{a^{2} x^{2} - 1}}{567 a^{3}} - \frac{16 c^{2} d^{2} \sqrt{a^{2} x^{2} - 1}}{25 a^{5}} - \frac{32 c d^{3} x^{2} \sqrt{a^{2} x^{2} - 1}}{245 a^{5}} - \frac{16 d^{4} x^{4} \sqrt{a^{2} x^{2} - 1}}{945 a^{5}} - \frac{64 c d^{3} \sqrt{a^{2} x^{2} - 1}}{245 a^{7}} - \frac{64 d^{4} x^{2} \sqrt{a^{2} x^{2} - 1}}{2835 a^{7}} - \frac{128 d^{4} \sqrt{a^{2} x^{2} - 1}}{2835 a^{9}} & \text{for}\: a \neq 0 \\\frac{i \pi \left(c^{4} x + \frac{4 c^{3} d x^{3}}{3} + \frac{6 c^{2} d^{2} x^{5}}{5} + \frac{4 c d^{3} x^{7}}{7} + \frac{d^{4} x^{9}}{9}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*acosh(a*x) + 4*c**3*d*x**3*acosh(a*x)/3 + 6*c**2*d**2*x**5*acosh(a*x)/5 + 4*c*d**3*x**7*acosh(a*x)/7 + d**4*x**9*acosh(a*x)/9 - c**4*sqrt(a**2*x**2 - 1)/a - 4*c**3*d*x**2*sqrt(a**2*x**2 - 1)/(9*a) - 6*c**2*d**2*x**4*sqrt(a**2*x**2 - 1)/(25*a) - 4*c*d**3*x**6*sqrt(a**2*x**2 - 1)/(49*a) - d**4*x**8*sqrt(a**2*x**2 - 1)/(81*a) - 8*c**3*d*sqrt(a**2*x**2 - 1)/(9*a**3) - 8*c**2*d**2*x**2*sqrt(a**2*x**2 - 1)/(25*a**3) - 24*c*d**3*x**4*sqrt(a**2*x**2 - 1)/(245*a**3) - 8*d**4*x**6*sqrt(a**2*x**2 - 1)/(567*a**3) - 16*c**2*d**2*sqrt(a**2*x**2 - 1)/(25*a**5) - 32*c*d**3*x**2*sqrt(a**2*x**2 - 1)/(245*a**5) - 16*d**4*x**4*sqrt(a**2*x**2 - 1)/(945*a**5) - 64*c*d**3*sqrt(a**2*x**2 - 1)/(245*a**7) - 64*d**4*x**2*sqrt(a**2*x**2 - 1)/(2835*a**7) - 128*d**4*sqrt(a**2*x**2 - 1)/(2835*a**9), Ne(a, 0)), (I*pi*(c**4*x + 4*c**3*d*x**3/3 + 6*c**2*d**2*x**5/5 + 4*c*d**3*x**7/7 + d**4*x**9/9)/2, True))","A",0
42,1,328,0,6.163049," ","integrate((d*x**2+c)**3*acosh(a*x),x)","\begin{cases} c^{3} x \operatorname{acosh}{\left(a x \right)} + c^{2} d x^{3} \operatorname{acosh}{\left(a x \right)} + \frac{3 c d^{2} x^{5} \operatorname{acosh}{\left(a x \right)}}{5} + \frac{d^{3} x^{7} \operatorname{acosh}{\left(a x \right)}}{7} - \frac{c^{3} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{c^{2} d x^{2} \sqrt{a^{2} x^{2} - 1}}{3 a} - \frac{3 c d^{2} x^{4} \sqrt{a^{2} x^{2} - 1}}{25 a} - \frac{d^{3} x^{6} \sqrt{a^{2} x^{2} - 1}}{49 a} - \frac{2 c^{2} d \sqrt{a^{2} x^{2} - 1}}{3 a^{3}} - \frac{4 c d^{2} x^{2} \sqrt{a^{2} x^{2} - 1}}{25 a^{3}} - \frac{6 d^{3} x^{4} \sqrt{a^{2} x^{2} - 1}}{245 a^{3}} - \frac{8 c d^{2} \sqrt{a^{2} x^{2} - 1}}{25 a^{5}} - \frac{8 d^{3} x^{2} \sqrt{a^{2} x^{2} - 1}}{245 a^{5}} - \frac{16 d^{3} \sqrt{a^{2} x^{2} - 1}}{245 a^{7}} & \text{for}\: a \neq 0 \\\frac{i \pi \left(c^{3} x + c^{2} d x^{3} + \frac{3 c d^{2} x^{5}}{5} + \frac{d^{3} x^{7}}{7}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*x*acosh(a*x) + c**2*d*x**3*acosh(a*x) + 3*c*d**2*x**5*acosh(a*x)/5 + d**3*x**7*acosh(a*x)/7 - c**3*sqrt(a**2*x**2 - 1)/a - c**2*d*x**2*sqrt(a**2*x**2 - 1)/(3*a) - 3*c*d**2*x**4*sqrt(a**2*x**2 - 1)/(25*a) - d**3*x**6*sqrt(a**2*x**2 - 1)/(49*a) - 2*c**2*d*sqrt(a**2*x**2 - 1)/(3*a**3) - 4*c*d**2*x**2*sqrt(a**2*x**2 - 1)/(25*a**3) - 6*d**3*x**4*sqrt(a**2*x**2 - 1)/(245*a**3) - 8*c*d**2*sqrt(a**2*x**2 - 1)/(25*a**5) - 8*d**3*x**2*sqrt(a**2*x**2 - 1)/(245*a**5) - 16*d**3*sqrt(a**2*x**2 - 1)/(245*a**7), Ne(a, 0)), (I*pi*(c**3*x + c**2*d*x**3 + 3*c*d**2*x**5/5 + d**3*x**7/7)/2, True))","A",0
43,1,199,0,2.104030," ","integrate((d*x**2+c)**2*acosh(a*x),x)","\begin{cases} c^{2} x \operatorname{acosh}{\left(a x \right)} + \frac{2 c d x^{3} \operatorname{acosh}{\left(a x \right)}}{3} + \frac{d^{2} x^{5} \operatorname{acosh}{\left(a x \right)}}{5} - \frac{c^{2} \sqrt{a^{2} x^{2} - 1}}{a} - \frac{2 c d x^{2} \sqrt{a^{2} x^{2} - 1}}{9 a} - \frac{d^{2} x^{4} \sqrt{a^{2} x^{2} - 1}}{25 a} - \frac{4 c d \sqrt{a^{2} x^{2} - 1}}{9 a^{3}} - \frac{4 d^{2} x^{2} \sqrt{a^{2} x^{2} - 1}}{75 a^{3}} - \frac{8 d^{2} \sqrt{a^{2} x^{2} - 1}}{75 a^{5}} & \text{for}\: a \neq 0 \\\frac{i \pi \left(c^{2} x + \frac{2 c d x^{3}}{3} + \frac{d^{2} x^{5}}{5}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x*acosh(a*x) + 2*c*d*x**3*acosh(a*x)/3 + d**2*x**5*acosh(a*x)/5 - c**2*sqrt(a**2*x**2 - 1)/a - 2*c*d*x**2*sqrt(a**2*x**2 - 1)/(9*a) - d**2*x**4*sqrt(a**2*x**2 - 1)/(25*a) - 4*c*d*sqrt(a**2*x**2 - 1)/(9*a**3) - 4*d**2*x**2*sqrt(a**2*x**2 - 1)/(75*a**3) - 8*d**2*sqrt(a**2*x**2 - 1)/(75*a**5), Ne(a, 0)), (I*pi*(c**2*x + 2*c*d*x**3/3 + d**2*x**5/5)/2, True))","A",0
44,1,90,0,0.508638," ","integrate((d*x**2+c)*acosh(a*x),x)","\begin{cases} c x \operatorname{acosh}{\left(a x \right)} + \frac{d x^{3} \operatorname{acosh}{\left(a x \right)}}{3} - \frac{c \sqrt{a^{2} x^{2} - 1}}{a} - \frac{d x^{2} \sqrt{a^{2} x^{2} - 1}}{9 a} - \frac{2 d \sqrt{a^{2} x^{2} - 1}}{9 a^{3}} & \text{for}\: a \neq 0 \\\frac{i \pi \left(c x + \frac{d x^{3}}{3}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x*acosh(a*x) + d*x**3*acosh(a*x)/3 - c*sqrt(a**2*x**2 - 1)/a - d*x**2*sqrt(a**2*x**2 - 1)/(9*a) - 2*d*sqrt(a**2*x**2 - 1)/(9*a**3), Ne(a, 0)), (I*pi*(c*x + d*x**3/3)/2, True))","A",0
45,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c),x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{c + d x^{2}}\, dx"," ",0,"Integral(acosh(a*x)/(c + d*x**2), x)","F",0
46,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**2,x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(acosh(a*x)/(c + d*x**2)**2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)*acosh(a*x),x)","\int \sqrt{c + d x^{2}} \operatorname{acosh}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)*acosh(a*x), x)","F",0
48,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**(1/2),x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(acosh(a*x)/sqrt(c + d*x**2), x)","F",0
49,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**(3/2),x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(acosh(a*x)/(c + d*x**2)**(3/2), x)","F",0
50,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**(5/2),x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(acosh(a*x)/(c + d*x**2)**(5/2), x)","F",0
51,0,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**(7/2),x)","\int \frac{\operatorname{acosh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(acosh(a*x)/(c + d*x**2)**(7/2), x)","F",0
52,-1,0,0,0.000000," ","integrate(acosh(a*x)/(d*x**2+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*acosh(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))*(f + g*x)**3, x)","F",0
54,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*acosh(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))*(f + g*x)**2, x)","F",0
55,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))*(f + g*x), x)","F",0
56,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))*(-c**2*d*x**2+d)**(1/2)/(g*x+f),x)","\int \frac{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))/(f + g*x), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))*(-c**2*d*x**2+d)**(1/2)/(g*x+f)**2,x)","\int \frac{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right)}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))/(f + g*x)**2, x)","F",0
58,0,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(3/2)*(a+b*acosh(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*acosh(c*x))*(f + g*x)**3, x)","F",0
59,0,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(3/2)*(a+b*acosh(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*acosh(c*x))*(f + g*x)**2, x)","F",0
60,0,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(3/2)*(a+b*acosh(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*acosh(c*x))*(f + g*x), x)","F",0
61,0,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(3/2)*(a+b*acosh(c*x))/(g*x+f),x)","\int \frac{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*acosh(c*x))/(f + g*x), x)","F",0
62,-1,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(5/2)*(a+b*acosh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(5/2)*(a+b*acosh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(5/2)*(a+b*acosh(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,0,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(5/2)*(a+b*acosh(c*x))/(g*x+f),x)","\int \frac{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{acosh}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(5/2)*(a + b*acosh(c*x))/(f + g*x), x)","F",0
66,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{3}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)**3/sqrt(-d*(c*x - 1)*(c*x + 1)), x)","F",0
67,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{2}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)**2/sqrt(-d*(c*x - 1)*(c*x + 1)), x)","F",0
68,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)/sqrt(-d*(c*x - 1)*(c*x + 1)), x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(g*x+f)/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)), x)","F",0
70,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(g*x+f)**2/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(c*x))/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)**2), x)","F",0
71,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{3}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)**3/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)**2/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \left(f + g x\right)}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*(f + g*x)/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))/(g*x+f)/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c x \right)}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*acosh(c*x))/((-d*(c*x - 1)*(c*x + 1))**(3/2)*(f + g*x)), x)","F",0
75,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))**n/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{n} \left(f + g x\right)}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**n*(f + g*x)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
76,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))**n/(-c*x+1)**(1/2)/(c*x+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{n} \left(f + g x\right)}{\sqrt{- c x + 1} \sqrt{c x + 1}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**n*(f + g*x)/(sqrt(-c*x + 1)*sqrt(c*x + 1)), x)","F",0
77,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*acosh(c*x))**n/(c*d1*x+d1)**(1/2)/(-c*d2*x+d2)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{n} \left(f + g x\right)}{\sqrt{d_{1} \left(c x + 1\right)} \sqrt{- d_{2} \left(c x - 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**n*(f + g*x)/(sqrt(d1*(c*x + 1))*sqrt(-d2*(c*x - 1))), x)","F",0
78,-1,0,0,0.000000," ","integrate((a+b*acosh(c*x))**n*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))**2*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right)^{2} \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))**2*log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
80,0,0,0,0.000000," ","integrate((a+b*acosh(c*x))*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c x \right)}\right) \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*acosh(c*x))*log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
81,0,0,0,0.000000," ","integrate(ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
82,0,0,0,0.000000," ","integrate(ln(h*(g*x+f)**m)/(a+b*acosh(c*x))/(-c**2*x**2+1)**(1/2),x)","\int \frac{\log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{acosh}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/(sqrt(-(c*x - 1)*(c*x + 1))*(a + b*acosh(c*x))), x)","F",0
83,1,255,0,1.385043," ","integrate(x**3*acosh(b*x+a),x)","\begin{cases} - \frac{a^{4} \operatorname{acosh}{\left(a + b x \right)}}{4 b^{4}} + \frac{25 a^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{48 b^{4}} - \frac{13 a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{48 b^{3}} - \frac{3 a^{2} \operatorname{acosh}{\left(a + b x \right)}}{4 b^{4}} + \frac{7 a x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{48 b^{2}} + \frac{55 a \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{96 b^{4}} + \frac{x^{4} \operatorname{acosh}{\left(a + b x \right)}}{4} - \frac{x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{16 b} - \frac{3 x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{32 b^{3}} - \frac{3 \operatorname{acosh}{\left(a + b x \right)}}{32 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{acosh}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*acosh(a + b*x)/(4*b**4) + 25*a**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(48*b**4) - 13*a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(48*b**3) - 3*a**2*acosh(a + b*x)/(4*b**4) + 7*a*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(48*b**2) + 55*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(96*b**4) + x**4*acosh(a + b*x)/4 - x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(16*b) - 3*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(32*b**3) - 3*acosh(a + b*x)/(32*b**4), Ne(b, 0)), (x**4*acosh(a)/4, True))","A",0
84,1,170,0,0.672578," ","integrate(x**2*acosh(b*x+a),x)","\begin{cases} \frac{a^{3} \operatorname{acosh}{\left(a + b x \right)}}{3 b^{3}} - \frac{11 a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{18 b^{3}} + \frac{5 a x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{18 b^{2}} + \frac{a \operatorname{acosh}{\left(a + b x \right)}}{2 b^{3}} + \frac{x^{3} \operatorname{acosh}{\left(a + b x \right)}}{3} - \frac{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{9 b} - \frac{2 \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{9 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{acosh}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*acosh(a + b*x)/(3*b**3) - 11*a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(18*b**3) + 5*a*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(18*b**2) + a*acosh(a + b*x)/(2*b**3) + x**3*acosh(a + b*x)/3 - x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(9*b) - 2*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(9*b**3), Ne(b, 0)), (x**3*acosh(a)/3, True))","A",0
85,1,104,0,0.289739," ","integrate(x*acosh(b*x+a),x)","\begin{cases} - \frac{a^{2} \operatorname{acosh}{\left(a + b x \right)}}{2 b^{2}} + \frac{3 a \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{4 b^{2}} + \frac{x^{2} \operatorname{acosh}{\left(a + b x \right)}}{2} - \frac{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{4 b} - \frac{\operatorname{acosh}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{acosh}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*acosh(a + b*x)/(2*b**2) + 3*a*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(4*b**2) + x**2*acosh(a + b*x)/2 - x*sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/(4*b) - acosh(a + b*x)/(4*b**2), Ne(b, 0)), (x**2*acosh(a)/2, True))","A",0
86,1,46,0,0.152883," ","integrate(acosh(b*x+a),x)","\begin{cases} \frac{a \operatorname{acosh}{\left(a + b x \right)}}{b} + x \operatorname{acosh}{\left(a + b x \right)} - \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} - 1}}{b} & \text{for}\: b \neq 0 \\x \operatorname{acosh}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*acosh(a + b*x)/b + x*acosh(a + b*x) - sqrt(a**2 + 2*a*b*x + b**2*x**2 - 1)/b, Ne(b, 0)), (x*acosh(a), True))","A",0
87,0,0,0,0.000000," ","integrate(acosh(b*x+a)/x,x)","\int \frac{\operatorname{acosh}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(acosh(a + b*x)/x, x)","F",0
88,0,0,0,0.000000," ","integrate(acosh(b*x+a)/x**2,x)","\int \frac{\operatorname{acosh}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(acosh(a + b*x)/x**2, x)","F",0
89,0,0,0,0.000000," ","integrate(acosh(b*x+a)/x**3,x)","\int \frac{\operatorname{acosh}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(acosh(a + b*x)/x**3, x)","F",0
90,0,0,0,0.000000," ","integrate(acosh(b*x+a)/x**4,x)","\int \frac{\operatorname{acosh}{\left(a + b x \right)}}{x^{4}}\, dx"," ",0,"Integral(acosh(a + b*x)/x**4, x)","F",0
91,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*acosh(c + d*x)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(a-b*acosh(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a - b \operatorname{acosh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a - b*acosh(c + d*x)), x)","F",0
93,1,527,0,3.251047," ","integrate((d*e*x+c*e)**4*(a+b*acosh(d*x+c)),x)","\begin{cases} a c^{4} e^{4} x + 2 a c^{3} d e^{4} x^{2} + 2 a c^{2} d^{2} e^{4} x^{3} + a c d^{3} e^{4} x^{4} + \frac{a d^{4} e^{4} x^{5}}{5} + \frac{b c^{5} e^{4} \operatorname{acosh}{\left(c + d x \right)}}{5 d} + b c^{4} e^{4} x \operatorname{acosh}{\left(c + d x \right)} - \frac{b c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25 d} + 2 b c^{3} d e^{4} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{4 b c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} + 2 b c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{6 b c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{4 b c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75 d} + b c d^{3} e^{4} x^{4} \operatorname{acosh}{\left(c + d x \right)} - \frac{4 b c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{8 b c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75} + \frac{b d^{4} e^{4} x^{5} \operatorname{acosh}{\left(c + d x \right)}}{5} - \frac{b d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{4 b d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75} - \frac{8 b e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{acosh}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*e**4*x + 2*a*c**3*d*e**4*x**2 + 2*a*c**2*d**2*e**4*x**3 + a*c*d**3*e**4*x**4 + a*d**4*e**4*x**5/5 + b*c**5*e**4*acosh(c + d*x)/(5*d) + b*c**4*e**4*x*acosh(c + d*x) - b*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(25*d) + 2*b*c**3*d*e**4*x**2*acosh(c + d*x) - 4*b*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 + 2*b*c**2*d**2*e**4*x**3*acosh(c + d*x) - 6*b*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 4*b*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(75*d) + b*c*d**3*e**4*x**4*acosh(c + d*x) - 4*b*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 8*b*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/75 + b*d**4*e**4*x**5*acosh(c + d*x)/5 - b*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 4*b*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/75 - 8*b*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(75*d), Ne(d, 0)), (c**4*e**4*x*(a + b*acosh(c)), True))","A",0
94,1,394,0,1.599298," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c)),x)","\begin{cases} a c^{3} e^{3} x + \frac{3 a c^{2} d e^{3} x^{2}}{2} + a c d^{2} e^{3} x^{3} + \frac{a d^{3} e^{3} x^{4}}{4} + \frac{b c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{4 d} + b c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{b c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16 d} + \frac{3 b c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{3 b c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} + b c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 b c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} - \frac{3 b c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32 d} + \frac{b d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{4} - \frac{b d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} - \frac{3 b e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32} - \frac{3 b e^{3} \operatorname{acosh}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{acosh}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*e**3*x + 3*a*c**2*d*e**3*x**2/2 + a*c*d**2*e**3*x**3 + a*d**3*e**3*x**4/4 + b*c**4*e**3*acosh(c + d*x)/(4*d) + b*c**3*e**3*x*acosh(c + d*x) - b*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(16*d) + 3*b*c**2*d*e**3*x**2*acosh(c + d*x)/2 - 3*b*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 + b*c*d**2*e**3*x**3*acosh(c + d*x) - 3*b*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 - 3*b*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(32*d) + b*d**3*e**3*x**4*acosh(c + d*x)/4 - b*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 - 3*b*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/32 - 3*b*e**3*acosh(c + d*x)/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*acosh(c)), True))","A",0
95,1,258,0,0.728952," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c)),x)","\begin{cases} a c^{2} e^{2} x + a c d e^{2} x^{2} + \frac{a d^{2} e^{2} x^{3}}{3} + \frac{b c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + b c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)} - \frac{b c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} + b c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{2 b c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} + \frac{b d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{b d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} - \frac{2 b e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{acosh}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*e**2*x + a*c*d*e**2*x**2 + a*d**2*e**2*x**3/3 + b*c**3*e**2*acosh(c + d*x)/(3*d) + b*c**2*e**2*x*acosh(c + d*x) - b*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d) + b*c*d*e**2*x**2*acosh(c + d*x) - 2*b*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 + b*d**2*e**2*x**3*acosh(c + d*x)/3 - b*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 - 2*b*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d), Ne(d, 0)), (c**2*e**2*x*(a + b*acosh(c)), True))","A",0
96,1,148,0,0.314867," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c)),x)","\begin{cases} a c e x + \frac{a d e x^{2}}{2} + \frac{b c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{2 d} + b c e x \operatorname{acosh}{\left(c + d x \right)} - \frac{b c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4 d} + \frac{b d e x^{2} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{b e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4} - \frac{b e \operatorname{acosh}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{acosh}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*e*x + a*d*e*x**2/2 + b*c**2*e*acosh(c + d*x)/(2*d) + b*c*e*x*acosh(c + d*x) - b*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(4*d) + b*d*e*x**2*acosh(c + d*x)/2 - b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/4 - b*e*acosh(c + d*x)/(4*d), Ne(d, 0)), (c*e*x*(a + b*acosh(c)), True))","A",0
97,1,51,0,0.151175," ","integrate(a+b*acosh(d*x+c),x)","a x + b \left(\begin{cases} \frac{c \operatorname{acosh}{\left(c + d x \right)}}{d} + x \operatorname{acosh}{\left(c + d x \right)} - \frac{\sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} & \text{for}\: d \neq 0 \\x \operatorname{acosh}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((c*acosh(c + d*x)/d + x*acosh(c + d*x) - sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d, Ne(d, 0)), (x*acosh(c), True))","A",0
98,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e),x)","\frac{\int \frac{a}{c + d x}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a/(c + d*x), x) + Integral(b*acosh(c + d*x)/(c + d*x), x))/e","F",0
99,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**2,x)","\frac{\int \frac{a}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b*acosh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
100,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**3,x)","\frac{\int \frac{a}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b*acosh(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
101,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**4,x)","\frac{\int \frac{a}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b*acosh(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
102,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**5,x)","\frac{\int \frac{a}{c^{5} + 5 c^{4} d x + 10 c^{3} d^{2} x^{2} + 10 c^{2} d^{3} x^{3} + 5 c d^{4} x^{4} + d^{5} x^{5}}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c^{5} + 5 c^{4} d x + 10 c^{3} d^{2} x^{2} + 10 c^{2} d^{3} x^{3} + 5 c d^{4} x^{4} + d^{5} x^{5}}\, dx}{e^{5}}"," ",0,"(Integral(a/(c**5 + 5*c**4*d*x + 10*c**3*d**2*x**2 + 10*c**2*d**3*x**3 + 5*c*d**4*x**4 + d**5*x**5), x) + Integral(b*acosh(c + d*x)/(c**5 + 5*c**4*d*x + 10*c**3*d**2*x**2 + 10*c**2*d**3*x**3 + 5*c*d**4*x**4 + d**5*x**5), x))/e**5","F",0
103,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**6,x)","\frac{\int \frac{a}{c^{6} + 6 c^{5} d x + 15 c^{4} d^{2} x^{2} + 20 c^{3} d^{3} x^{3} + 15 c^{2} d^{4} x^{4} + 6 c d^{5} x^{5} + d^{6} x^{6}}\, dx + \int \frac{b \operatorname{acosh}{\left(c + d x \right)}}{c^{6} + 6 c^{5} d x + 15 c^{4} d^{2} x^{2} + 20 c^{3} d^{3} x^{3} + 15 c^{2} d^{4} x^{4} + 6 c d^{5} x^{5} + d^{6} x^{6}}\, dx}{e^{6}}"," ",0,"(Integral(a/(c**6 + 6*c**5*d*x + 15*c**4*d**2*x**2 + 20*c**3*d**3*x**3 + 15*c**2*d**4*x**4 + 6*c*d**5*x**5 + d**6*x**6), x) + Integral(b*acosh(c + d*x)/(c**6 + 6*c**5*d*x + 15*c**4*d**2*x**2 + 20*c**3*d**3*x**3 + 15*c**2*d**4*x**4 + 6*c*d**5*x**5 + d**6*x**6), x))/e**6","F",0
104,1,1268,0,7.033158," ","integrate((d*e*x+c*e)**4*(a+b*acosh(d*x+c))**2,x)","\begin{cases} a^{2} c^{4} e^{4} x + 2 a^{2} c^{3} d e^{4} x^{2} + 2 a^{2} c^{2} d^{2} e^{4} x^{3} + a^{2} c d^{3} e^{4} x^{4} + \frac{a^{2} d^{4} e^{4} x^{5}}{5} + \frac{2 a b c^{5} e^{4} \operatorname{acosh}{\left(c + d x \right)}}{5 d} + 2 a b c^{4} e^{4} x \operatorname{acosh}{\left(c + d x \right)} - \frac{2 a b c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25 d} + 4 a b c^{3} d e^{4} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{8 a b c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} + 4 a b c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{12 a b c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{8 a b c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75 d} + 2 a b c d^{3} e^{4} x^{4} \operatorname{acosh}{\left(c + d x \right)} - \frac{8 a b c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{16 a b c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75} + \frac{2 a b d^{4} e^{4} x^{5} \operatorname{acosh}{\left(c + d x \right)}}{5} - \frac{2 a b d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{8 a b d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75} - \frac{16 a b e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{75 d} + \frac{b^{2} c^{5} e^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{5 d} + b^{2} c^{4} e^{4} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 b^{2} c^{4} e^{4} x}{25} - \frac{2 b^{2} c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25 d} + 2 b^{2} c^{3} d e^{4} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{4 b^{2} c^{3} d e^{4} x^{2}}{25} - \frac{8 b^{2} c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + 2 b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{4 b^{2} c^{2} d^{2} e^{4} x^{3}}{25} - \frac{12 b^{2} c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 b^{2} c^{2} e^{4} x}{75} - \frac{8 b^{2} c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{75 d} + b^{2} c d^{3} e^{4} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 b^{2} c d^{3} e^{4} x^{4}}{25} - \frac{8 b^{2} c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 b^{2} c d e^{4} x^{2}}{75} - \frac{16 b^{2} c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{75} + \frac{b^{2} d^{4} e^{4} x^{5} \operatorname{acosh}^{2}{\left(c + d x \right)}}{5} + \frac{2 b^{2} d^{4} e^{4} x^{5}}{125} - \frac{2 b^{2} d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 b^{2} d^{2} e^{4} x^{3}}{225} - \frac{8 b^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{75} + \frac{16 b^{2} e^{4} x}{75} - \frac{16 b^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{75 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*e**4*x + 2*a**2*c**3*d*e**4*x**2 + 2*a**2*c**2*d**2*e**4*x**3 + a**2*c*d**3*e**4*x**4 + a**2*d**4*e**4*x**5/5 + 2*a*b*c**5*e**4*acosh(c + d*x)/(5*d) + 2*a*b*c**4*e**4*x*acosh(c + d*x) - 2*a*b*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(25*d) + 4*a*b*c**3*d*e**4*x**2*acosh(c + d*x) - 8*a*b*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 + 4*a*b*c**2*d**2*e**4*x**3*acosh(c + d*x) - 12*a*b*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 8*a*b*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(75*d) + 2*a*b*c*d**3*e**4*x**4*acosh(c + d*x) - 8*a*b*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 16*a*b*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/75 + 2*a*b*d**4*e**4*x**5*acosh(c + d*x)/5 - 2*a*b*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 8*a*b*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/75 - 16*a*b*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(75*d) + b**2*c**5*e**4*acosh(c + d*x)**2/(5*d) + b**2*c**4*e**4*x*acosh(c + d*x)**2 + 2*b**2*c**4*e**4*x/25 - 2*b**2*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(25*d) + 2*b**2*c**3*d*e**4*x**2*acosh(c + d*x)**2 + 4*b**2*c**3*d*e**4*x**2/25 - 8*b**2*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 2*b**2*c**2*d**2*e**4*x**3*acosh(c + d*x)**2 + 4*b**2*c**2*d**2*e**4*x**3/25 - 12*b**2*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*b**2*c**2*e**4*x/75 - 8*b**2*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(75*d) + b**2*c*d**3*e**4*x**4*acosh(c + d*x)**2 + 2*b**2*c*d**3*e**4*x**4/25 - 8*b**2*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*b**2*c*d*e**4*x**2/75 - 16*b**2*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/75 + b**2*d**4*e**4*x**5*acosh(c + d*x)**2/5 + 2*b**2*d**4*e**4*x**5/125 - 2*b**2*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*b**2*d**2*e**4*x**3/225 - 8*b**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/75 + 16*b**2*e**4*x/75 - 16*b**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(75*d), Ne(d, 0)), (c**4*e**4*x*(a + b*acosh(c))**2, True))","A",0
105,1,916,0,4.316826," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**2,x)","\begin{cases} a^{2} c^{3} e^{3} x + \frac{3 a^{2} c^{2} d e^{3} x^{2}}{2} + a^{2} c d^{2} e^{3} x^{3} + \frac{a^{2} d^{3} e^{3} x^{4}}{4} + \frac{a b c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{2 d} + 2 a b c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{a b c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8 d} + 3 a b c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a b c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8} + 2 a b c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a b c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8} - \frac{3 a b c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16 d} + \frac{a b d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{a b d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8} - \frac{3 a b e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} - \frac{3 a b e^{3} \operatorname{acosh}{\left(c + d x \right)}}{16 d} + \frac{b^{2} c^{4} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} + b^{2} c^{3} e^{3} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{b^{2} c^{3} e^{3} x}{8} - \frac{b^{2} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + \frac{3 b^{2} c^{2} d e^{3} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{3 b^{2} c^{2} d e^{3} x^{2}}{16} - \frac{3 b^{2} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + b^{2} c d^{2} e^{3} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{b^{2} c d^{2} e^{3} x^{3}}{8} - \frac{3 b^{2} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + \frac{3 b^{2} c e^{3} x}{16} - \frac{3 b^{2} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{16 d} + \frac{b^{2} d^{3} e^{3} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} + \frac{b^{2} d^{3} e^{3} x^{4}}{32} - \frac{b^{2} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + \frac{3 b^{2} d e^{3} x^{2}}{32} - \frac{3 b^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{16} - \frac{3 b^{2} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*e**3*x + 3*a**2*c**2*d*e**3*x**2/2 + a**2*c*d**2*e**3*x**3 + a**2*d**3*e**3*x**4/4 + a*b*c**4*e**3*acosh(c + d*x)/(2*d) + 2*a*b*c**3*e**3*x*acosh(c + d*x) - a*b*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(8*d) + 3*a*b*c**2*d*e**3*x**2*acosh(c + d*x) - 3*a*b*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/8 + 2*a*b*c*d**2*e**3*x**3*acosh(c + d*x) - 3*a*b*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/8 - 3*a*b*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(16*d) + a*b*d**3*e**3*x**4*acosh(c + d*x)/2 - a*b*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/8 - 3*a*b*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 - 3*a*b*e**3*acosh(c + d*x)/(16*d) + b**2*c**4*e**3*acosh(c + d*x)**2/(4*d) + b**2*c**3*e**3*x*acosh(c + d*x)**2 + b**2*c**3*e**3*x/8 - b**2*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(8*d) + 3*b**2*c**2*d*e**3*x**2*acosh(c + d*x)**2/2 + 3*b**2*c**2*d*e**3*x**2/16 - 3*b**2*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + b**2*c*d**2*e**3*x**3*acosh(c + d*x)**2 + b**2*c*d**2*e**3*x**3/8 - 3*b**2*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + 3*b**2*c*e**3*x/16 - 3*b**2*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(16*d) + b**2*d**3*e**3*x**4*acosh(c + d*x)**2/4 + b**2*d**3*e**3*x**4/32 - b**2*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + 3*b**2*d*e**3*x**2/32 - 3*b**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/16 - 3*b**2*e**3*acosh(c + d*x)**2/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*acosh(c))**2, True))","A",0
106,1,610,0,1.778251," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**2,x)","\begin{cases} a^{2} c^{2} e^{2} x + a^{2} c d e^{2} x^{2} + \frac{a^{2} d^{2} e^{2} x^{3}}{3} + \frac{2 a b c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + 2 a b c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)} - \frac{2 a b c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} + 2 a b c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{4 a b c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} + \frac{2 a b d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{2 a b d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} - \frac{4 a b e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} + \frac{b^{2} c^{3} e^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} + b^{2} c^{2} e^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 b^{2} c^{2} e^{2} x}{9} - \frac{2 b^{2} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{9 d} + b^{2} c d e^{2} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 b^{2} c d e^{2} x^{2}}{9} - \frac{4 b^{2} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{9} + \frac{b^{2} d^{2} e^{2} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} + \frac{2 b^{2} d^{2} e^{2} x^{3}}{27} - \frac{2 b^{2} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{9} + \frac{4 b^{2} e^{2} x}{9} - \frac{4 b^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*e**2*x + a**2*c*d*e**2*x**2 + a**2*d**2*e**2*x**3/3 + 2*a*b*c**3*e**2*acosh(c + d*x)/(3*d) + 2*a*b*c**2*e**2*x*acosh(c + d*x) - 2*a*b*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d) + 2*a*b*c*d*e**2*x**2*acosh(c + d*x) - 4*a*b*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 + 2*a*b*d**2*e**2*x**3*acosh(c + d*x)/3 - 2*a*b*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 - 4*a*b*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d) + b**2*c**3*e**2*acosh(c + d*x)**2/(3*d) + b**2*c**2*e**2*x*acosh(c + d*x)**2 + 2*b**2*c**2*e**2*x/9 - 2*b**2*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(9*d) + b**2*c*d*e**2*x**2*acosh(c + d*x)**2 + 2*b**2*c*d*e**2*x**2/9 - 4*b**2*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/9 + b**2*d**2*e**2*x**3*acosh(c + d*x)**2/3 + 2*b**2*d**2*e**2*x**3/27 - 2*b**2*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/9 + 4*b**2*e**2*x/9 - 4*b**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(9*d), Ne(d, 0)), (c**2*e**2*x*(a + b*acosh(c))**2, True))","A",0
107,1,335,0,0.820528," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**2,x)","\begin{cases} a^{2} c e x + \frac{a^{2} d e x^{2}}{2} + \frac{a b c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{d} + 2 a b c e x \operatorname{acosh}{\left(c + d x \right)} - \frac{a b c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{2 d} + a b d e x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{a b e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{2} - \frac{a b e \operatorname{acosh}{\left(c + d x \right)}}{2 d} + \frac{b^{2} c^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{2 d} + b^{2} c e x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{b^{2} c e x}{2} - \frac{b^{2} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2 d} + \frac{b^{2} d e x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{b^{2} d e x^{2}}{4} - \frac{b^{2} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{b^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*e*x + a**2*d*e*x**2/2 + a*b*c**2*e*acosh(c + d*x)/d + 2*a*b*c*e*x*acosh(c + d*x) - a*b*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(2*d) + a*b*d*e*x**2*acosh(c + d*x) - a*b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/2 - a*b*e*acosh(c + d*x)/(2*d) + b**2*c**2*e*acosh(c + d*x)**2/(2*d) + b**2*c*e*x*acosh(c + d*x)**2 + b**2*c*e*x/2 - b**2*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(2*d) + b**2*d*e*x**2*acosh(c + d*x)**2/2 + b**2*d*e*x**2/4 - b**2*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/2 - b**2*e*acosh(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*acosh(c))**2, True))","A",0
108,1,143,0,0.304924," ","integrate((a+b*acosh(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{2 a b c \operatorname{acosh}{\left(c + d x \right)}}{d} + 2 a b x \operatorname{acosh}{\left(c + d x \right)} - \frac{2 a b \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} + \frac{b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + b^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + 2 b^{2} x - \frac{2 b^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*c*acosh(c + d*x)/d + 2*a*b*x*acosh(c + d*x) - 2*a*b*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d + b**2*c*acosh(c + d*x)**2/d + b**2*x*acosh(c + d*x)**2 + 2*b**2*x - 2*b**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/d, Ne(d, 0)), (x*(a + b*acosh(c))**2, True))","A",0
109,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e),x)","\frac{\int \frac{a^{2}}{c + d x}\, dx + \int \frac{b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2/(c + d*x), x) + Integral(b**2*acosh(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*acosh(c + d*x)/(c + d*x), x))/e","F",0
110,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{2}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{2 a b \operatorname{acosh}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**2*acosh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(2*a*b*acosh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
111,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{2}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{2 a b \operatorname{acosh}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**2*acosh(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(2*a*b*acosh(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
112,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{2}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{2 a b \operatorname{acosh}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**2*acosh(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(2*a*b*acosh(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
113,1,2518,0,16.245124," ","integrate((d*e*x+c*e)**4*(a+b*acosh(d*x+c))**3,x)","\begin{cases} a^{3} c^{4} e^{4} x + 2 a^{3} c^{3} d e^{4} x^{2} + 2 a^{3} c^{2} d^{2} e^{4} x^{3} + a^{3} c d^{3} e^{4} x^{4} + \frac{a^{3} d^{4} e^{4} x^{5}}{5} + \frac{3 a^{2} b c^{5} e^{4} \operatorname{acosh}{\left(c + d x \right)}}{5 d} + 3 a^{2} b c^{4} e^{4} x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{2} b c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25 d} + 6 a^{2} b c^{3} d e^{4} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{12 a^{2} b c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} + 6 a^{2} b c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{18 a^{2} b c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{4 a^{2} b c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25 d} + 3 a^{2} b c d^{3} e^{4} x^{4} \operatorname{acosh}{\left(c + d x \right)} - \frac{12 a^{2} b c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{8 a^{2} b c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} + \frac{3 a^{2} b d^{4} e^{4} x^{5} \operatorname{acosh}{\left(c + d x \right)}}{5} - \frac{3 a^{2} b d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{4 a^{2} b d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25} - \frac{8 a^{2} b e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{25 d} + \frac{3 a b^{2} c^{5} e^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{5 d} + 3 a b^{2} c^{4} e^{4} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{6 a b^{2} c^{4} e^{4} x}{25} - \frac{6 a b^{2} c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25 d} + 6 a b^{2} c^{3} d e^{4} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{12 a b^{2} c^{3} d e^{4} x^{2}}{25} - \frac{24 a b^{2} c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + 6 a b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{12 a b^{2} c^{2} d^{2} e^{4} x^{3}}{25} - \frac{36 a b^{2} c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 a b^{2} c^{2} e^{4} x}{25} - \frac{8 a b^{2} c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25 d} + 3 a b^{2} c d^{3} e^{4} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{6 a b^{2} c d^{3} e^{4} x^{4}}{25} - \frac{24 a b^{2} c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 a b^{2} c d e^{4} x^{2}}{25} - \frac{16 a b^{2} c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{3 a b^{2} d^{4} e^{4} x^{5} \operatorname{acosh}^{2}{\left(c + d x \right)}}{5} + \frac{6 a b^{2} d^{4} e^{4} x^{5}}{125} - \frac{6 a b^{2} d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{8 a b^{2} d^{2} e^{4} x^{3}}{75} - \frac{8 a b^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25} + \frac{16 a b^{2} e^{4} x}{25} - \frac{16 a b^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{25 d} + \frac{b^{3} c^{5} e^{4} \operatorname{acosh}^{3}{\left(c + d x \right)}}{5 d} + \frac{6 b^{3} c^{5} e^{4} \operatorname{acosh}{\left(c + d x \right)}}{125 d} + b^{3} c^{4} e^{4} x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{6 b^{3} c^{4} e^{4} x \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{3 b^{3} c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25 d} - \frac{6 b^{3} c^{4} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{625 d} + 2 b^{3} c^{3} d e^{4} x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{12 b^{3} c^{3} d e^{4} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{12 b^{3} c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{24 b^{3} c^{3} e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{625} + \frac{8 b^{3} c^{3} e^{4} \operatorname{acosh}{\left(c + d x \right)}}{75 d} + 2 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{12 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{18 b^{3} c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{36 b^{3} c^{2} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{625} + \frac{8 b^{3} c^{2} e^{4} x \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{4 b^{3} c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25 d} - \frac{272 b^{3} c^{2} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{5625 d} + b^{3} c d^{3} e^{4} x^{4} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{6 b^{3} c d^{3} e^{4} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{12 b^{3} c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{24 b^{3} c d^{2} e^{4} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{625} + \frac{8 b^{3} c d e^{4} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{8 b^{3} c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{544 b^{3} c e^{4} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{5625} + \frac{16 b^{3} c e^{4} \operatorname{acosh}{\left(c + d x \right)}}{25 d} + \frac{b^{3} d^{4} e^{4} x^{5} \operatorname{acosh}^{3}{\left(c + d x \right)}}{5} + \frac{6 b^{3} d^{4} e^{4} x^{5} \operatorname{acosh}{\left(c + d x \right)}}{125} - \frac{3 b^{3} d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{6 b^{3} d^{3} e^{4} x^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{625} + \frac{8 b^{3} d^{2} e^{4} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{75} - \frac{4 b^{3} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25} - \frac{272 b^{3} d e^{4} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{5625} + \frac{16 b^{3} e^{4} x \operatorname{acosh}{\left(c + d x \right)}}{25} - \frac{8 b^{3} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{25 d} - \frac{4144 b^{3} e^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{5625 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**4*e**4*x + 2*a**3*c**3*d*e**4*x**2 + 2*a**3*c**2*d**2*e**4*x**3 + a**3*c*d**3*e**4*x**4 + a**3*d**4*e**4*x**5/5 + 3*a**2*b*c**5*e**4*acosh(c + d*x)/(5*d) + 3*a**2*b*c**4*e**4*x*acosh(c + d*x) - 3*a**2*b*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(25*d) + 6*a**2*b*c**3*d*e**4*x**2*acosh(c + d*x) - 12*a**2*b*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 + 6*a**2*b*c**2*d**2*e**4*x**3*acosh(c + d*x) - 18*a**2*b*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 4*a**2*b*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(25*d) + 3*a**2*b*c*d**3*e**4*x**4*acosh(c + d*x) - 12*a**2*b*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 8*a**2*b*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 + 3*a**2*b*d**4*e**4*x**5*acosh(c + d*x)/5 - 3*a**2*b*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 4*a**2*b*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/25 - 8*a**2*b*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(25*d) + 3*a*b**2*c**5*e**4*acosh(c + d*x)**2/(5*d) + 3*a*b**2*c**4*e**4*x*acosh(c + d*x)**2 + 6*a*b**2*c**4*e**4*x/25 - 6*a*b**2*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(25*d) + 6*a*b**2*c**3*d*e**4*x**2*acosh(c + d*x)**2 + 12*a*b**2*c**3*d*e**4*x**2/25 - 24*a*b**2*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 6*a*b**2*c**2*d**2*e**4*x**3*acosh(c + d*x)**2 + 12*a*b**2*c**2*d**2*e**4*x**3/25 - 36*a*b**2*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*a*b**2*c**2*e**4*x/25 - 8*a*b**2*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(25*d) + 3*a*b**2*c*d**3*e**4*x**4*acosh(c + d*x)**2 + 6*a*b**2*c*d**3*e**4*x**4/25 - 24*a*b**2*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*a*b**2*c*d*e**4*x**2/25 - 16*a*b**2*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 3*a*b**2*d**4*e**4*x**5*acosh(c + d*x)**2/5 + 6*a*b**2*d**4*e**4*x**5/125 - 6*a*b**2*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 8*a*b**2*d**2*e**4*x**3/75 - 8*a*b**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/25 + 16*a*b**2*e**4*x/25 - 16*a*b**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(25*d) + b**3*c**5*e**4*acosh(c + d*x)**3/(5*d) + 6*b**3*c**5*e**4*acosh(c + d*x)/(125*d) + b**3*c**4*e**4*x*acosh(c + d*x)**3 + 6*b**3*c**4*e**4*x*acosh(c + d*x)/25 - 3*b**3*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(25*d) - 6*b**3*c**4*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(625*d) + 2*b**3*c**3*d*e**4*x**2*acosh(c + d*x)**3 + 12*b**3*c**3*d*e**4*x**2*acosh(c + d*x)/25 - 12*b**3*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 24*b**3*c**3*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/625 + 8*b**3*c**3*e**4*acosh(c + d*x)/(75*d) + 2*b**3*c**2*d**2*e**4*x**3*acosh(c + d*x)**3 + 12*b**3*c**2*d**2*e**4*x**3*acosh(c + d*x)/25 - 18*b**3*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 36*b**3*c**2*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/625 + 8*b**3*c**2*e**4*x*acosh(c + d*x)/25 - 4*b**3*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(25*d) - 272*b**3*c**2*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(5625*d) + b**3*c*d**3*e**4*x**4*acosh(c + d*x)**3 + 6*b**3*c*d**3*e**4*x**4*acosh(c + d*x)/25 - 12*b**3*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 24*b**3*c*d**2*e**4*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/625 + 8*b**3*c*d*e**4*x**2*acosh(c + d*x)/25 - 8*b**3*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 544*b**3*c*e**4*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/5625 + 16*b**3*c*e**4*acosh(c + d*x)/(25*d) + b**3*d**4*e**4*x**5*acosh(c + d*x)**3/5 + 6*b**3*d**4*e**4*x**5*acosh(c + d*x)/125 - 3*b**3*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 6*b**3*d**3*e**4*x**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/625 + 8*b**3*d**2*e**4*x**3*acosh(c + d*x)/75 - 4*b**3*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/25 - 272*b**3*d*e**4*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/5625 + 16*b**3*e**4*x*acosh(c + d*x)/25 - 8*b**3*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(25*d) - 4144*b**3*e**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(5625*d), Ne(d, 0)), (c**4*e**4*x*(a + b*acosh(c))**3, True))","A",0
114,1,1828,0,9.572814," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**3,x)","\begin{cases} a^{3} c^{3} e^{3} x + \frac{3 a^{3} c^{2} d e^{3} x^{2}}{2} + a^{3} c d^{2} e^{3} x^{3} + \frac{a^{3} d^{3} e^{3} x^{4}}{4} + \frac{3 a^{2} b c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{4 d} + 3 a^{2} b c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{2} b c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16 d} + \frac{9 a^{2} b c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{9 a^{2} b c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} + 3 a^{2} b c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{9 a^{2} b c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} - \frac{9 a^{2} b c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32 d} + \frac{3 a^{2} b d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{4} - \frac{3 a^{2} b d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{16} - \frac{9 a^{2} b e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32} - \frac{9 a^{2} b e^{3} \operatorname{acosh}{\left(c + d x \right)}}{32 d} + \frac{3 a b^{2} c^{4} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} + 3 a b^{2} c^{3} e^{3} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a b^{2} c^{3} e^{3} x}{8} - \frac{3 a b^{2} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + \frac{9 a b^{2} c^{2} d e^{3} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{9 a b^{2} c^{2} d e^{3} x^{2}}{16} - \frac{9 a b^{2} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + 3 a b^{2} c d^{2} e^{3} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a b^{2} c d^{2} e^{3} x^{3}}{8} - \frac{9 a b^{2} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + \frac{9 a b^{2} c e^{3} x}{16} - \frac{9 a b^{2} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{16 d} + \frac{3 a b^{2} d^{3} e^{3} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} + \frac{3 a b^{2} d^{3} e^{3} x^{4}}{32} - \frac{3 a b^{2} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} + \frac{9 a b^{2} d e^{3} x^{2}}{32} - \frac{9 a b^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{16} - \frac{9 a b^{2} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{32 d} + \frac{b^{3} c^{4} e^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4 d} + \frac{3 b^{3} c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{32 d} + b^{3} c^{3} e^{3} x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)}}{8} - \frac{3 b^{3} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16 d} - \frac{3 b^{3} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{128 d} + \frac{3 b^{3} c^{2} d e^{3} x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)}}{2} + \frac{9 b^{3} c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{128} + \frac{9 b^{3} c^{2} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{32 d} + b^{3} c d^{2} e^{3} x^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{8} - \frac{9 b^{3} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{128} + \frac{9 b^{3} c e^{3} x \operatorname{acosh}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{32 d} - \frac{45 b^{3} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{256 d} + \frac{b^{3} d^{3} e^{3} x^{4} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4} + \frac{3 b^{3} d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{32} - \frac{3 b^{3} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16} - \frac{3 b^{3} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{128} + \frac{9 b^{3} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{32} - \frac{9 b^{3} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{32} - \frac{45 b^{3} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{256} - \frac{3 b^{3} e^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{32 d} - \frac{45 b^{3} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{256 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**3*e**3*x + 3*a**3*c**2*d*e**3*x**2/2 + a**3*c*d**2*e**3*x**3 + a**3*d**3*e**3*x**4/4 + 3*a**2*b*c**4*e**3*acosh(c + d*x)/(4*d) + 3*a**2*b*c**3*e**3*x*acosh(c + d*x) - 3*a**2*b*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(16*d) + 9*a**2*b*c**2*d*e**3*x**2*acosh(c + d*x)/2 - 9*a**2*b*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 + 3*a**2*b*c*d**2*e**3*x**3*acosh(c + d*x) - 9*a**2*b*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 - 9*a**2*b*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(32*d) + 3*a**2*b*d**3*e**3*x**4*acosh(c + d*x)/4 - 3*a**2*b*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/16 - 9*a**2*b*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/32 - 9*a**2*b*e**3*acosh(c + d*x)/(32*d) + 3*a*b**2*c**4*e**3*acosh(c + d*x)**2/(4*d) + 3*a*b**2*c**3*e**3*x*acosh(c + d*x)**2 + 3*a*b**2*c**3*e**3*x/8 - 3*a*b**2*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(8*d) + 9*a*b**2*c**2*d*e**3*x**2*acosh(c + d*x)**2/2 + 9*a*b**2*c**2*d*e**3*x**2/16 - 9*a*b**2*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + 3*a*b**2*c*d**2*e**3*x**3*acosh(c + d*x)**2 + 3*a*b**2*c*d**2*e**3*x**3/8 - 9*a*b**2*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + 9*a*b**2*c*e**3*x/16 - 9*a*b**2*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(16*d) + 3*a*b**2*d**3*e**3*x**4*acosh(c + d*x)**2/4 + 3*a*b**2*d**3*e**3*x**4/32 - 3*a*b**2*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 + 9*a*b**2*d*e**3*x**2/32 - 9*a*b**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/16 - 9*a*b**2*e**3*acosh(c + d*x)**2/(32*d) + b**3*c**4*e**3*acosh(c + d*x)**3/(4*d) + 3*b**3*c**4*e**3*acosh(c + d*x)/(32*d) + b**3*c**3*e**3*x*acosh(c + d*x)**3 + 3*b**3*c**3*e**3*x*acosh(c + d*x)/8 - 3*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(16*d) - 3*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(128*d) + 3*b**3*c**2*d*e**3*x**2*acosh(c + d*x)**3/2 + 9*b**3*c**2*d*e**3*x**2*acosh(c + d*x)/16 - 9*b**3*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/16 - 9*b**3*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/128 + 9*b**3*c**2*e**3*acosh(c + d*x)/(32*d) + b**3*c*d**2*e**3*x**3*acosh(c + d*x)**3 + 3*b**3*c*d**2*e**3*x**3*acosh(c + d*x)/8 - 9*b**3*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/16 - 9*b**3*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/128 + 9*b**3*c*e**3*x*acosh(c + d*x)/16 - 9*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(32*d) - 45*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(256*d) + b**3*d**3*e**3*x**4*acosh(c + d*x)**3/4 + 3*b**3*d**3*e**3*x**4*acosh(c + d*x)/32 - 3*b**3*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/16 - 3*b**3*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/128 + 9*b**3*d*e**3*x**2*acosh(c + d*x)/32 - 9*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/32 - 45*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/256 - 3*b**3*e**3*acosh(c + d*x)**3/(32*d) - 45*b**3*e**3*acosh(c + d*x)/(256*d), Ne(d, 0)), (c**3*e**3*x*(a + b*acosh(c))**3, True))","A",0
115,1,1173,0,4.722937," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**3,x)","\begin{cases} a^{3} c^{2} e^{2} x + a^{3} c d e^{2} x^{2} + \frac{a^{3} d^{2} e^{2} x^{3}}{3} + \frac{a^{2} b c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{d} + 3 a^{2} b c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)} - \frac{a^{2} b c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{3 d} + 3 a^{2} b c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{2 a^{2} b c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{3} + a^{2} b d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{a^{2} b d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{3} - \frac{2 a^{2} b e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{3 d} + \frac{a b^{2} c^{3} e^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} c^{2} e^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 a b^{2} c^{2} e^{2} x}{3} - \frac{2 a b^{2} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + 3 a b^{2} c d e^{2} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 a b^{2} c d e^{2} x^{2}}{3} - \frac{4 a b^{2} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3} + a b^{2} d^{2} e^{2} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{2 a b^{2} d^{2} e^{2} x^{3}}{9} - \frac{2 a b^{2} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3} + \frac{4 a b^{2} e^{2} x}{3} - \frac{4 a b^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + \frac{b^{3} c^{3} e^{2} \operatorname{acosh}^{3}{\left(c + d x \right)}}{3 d} + \frac{2 b^{3} c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{9 d} + b^{3} c^{2} e^{2} x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{2 b^{3} c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{b^{3} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} - \frac{2 b^{3} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27 d} + b^{3} c d e^{2} x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{2 b^{3} c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{2 b^{3} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} - \frac{4 b^{3} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27} + \frac{4 b^{3} c e^{2} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + \frac{b^{3} d^{2} e^{2} x^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{3} + \frac{2 b^{3} d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{9} - \frac{b^{3} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} - \frac{2 b^{3} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27} + \frac{4 b^{3} e^{2} x \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{2 b^{3} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} - \frac{40 b^{3} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**2*e**2*x + a**3*c*d*e**2*x**2 + a**3*d**2*e**2*x**3/3 + a**2*b*c**3*e**2*acosh(c + d*x)/d + 3*a**2*b*c**2*e**2*x*acosh(c + d*x) - a**2*b*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(3*d) + 3*a**2*b*c*d*e**2*x**2*acosh(c + d*x) - 2*a**2*b*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/3 + a**2*b*d**2*e**2*x**3*acosh(c + d*x) - a**2*b*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/3 - 2*a**2*b*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(3*d) + a*b**2*c**3*e**2*acosh(c + d*x)**2/d + 3*a*b**2*c**2*e**2*x*acosh(c + d*x)**2 + 2*a*b**2*c**2*e**2*x/3 - 2*a*b**2*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(3*d) + 3*a*b**2*c*d*e**2*x**2*acosh(c + d*x)**2 + 2*a*b**2*c*d*e**2*x**2/3 - 4*a*b**2*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/3 + a*b**2*d**2*e**2*x**3*acosh(c + d*x)**2 + 2*a*b**2*d**2*e**2*x**3/9 - 2*a*b**2*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/3 + 4*a*b**2*e**2*x/3 - 4*a*b**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(3*d) + b**3*c**3*e**2*acosh(c + d*x)**3/(3*d) + 2*b**3*c**3*e**2*acosh(c + d*x)/(9*d) + b**3*c**2*e**2*x*acosh(c + d*x)**3 + 2*b**3*c**2*e**2*x*acosh(c + d*x)/3 - b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(3*d) - 2*b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(27*d) + b**3*c*d*e**2*x**2*acosh(c + d*x)**3 + 2*b**3*c*d*e**2*x**2*acosh(c + d*x)/3 - 2*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/3 - 4*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/27 + 4*b**3*c*e**2*acosh(c + d*x)/(3*d) + b**3*d**2*e**2*x**3*acosh(c + d*x)**3/3 + 2*b**3*d**2*e**2*x**3*acosh(c + d*x)/9 - b**3*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/3 - 2*b**3*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/27 + 4*b**3*e**2*x*acosh(c + d*x)/3 - 2*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(3*d) - 40*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(27*d), Ne(d, 0)), (c**2*e**2*x*(a + b*acosh(c))**3, True))","A",0
116,1,685,0,1.996722," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**3,x)","\begin{cases} a^{3} c e x + \frac{a^{3} d e x^{2}}{2} + \frac{3 a^{2} b c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{2 d} + 3 a^{2} b c e x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{2} b c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4 d} + \frac{3 a^{2} b d e x^{2} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{3 a^{2} b e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4} - \frac{3 a^{2} b e \operatorname{acosh}{\left(c + d x \right)}}{4 d} + \frac{3 a b^{2} c^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{2 d} + 3 a b^{2} c e x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a b^{2} c e x}{2} - \frac{3 a b^{2} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2 d} + \frac{3 a b^{2} d e x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{3 a b^{2} d e x^{2}}{4} - \frac{3 a b^{2} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{3 a b^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} + \frac{b^{3} c^{2} e \operatorname{acosh}^{3}{\left(c + d x \right)}}{2 d} + \frac{3 b^{3} c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{4 d} + b^{3} c e x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 b^{3} c e x \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{3 b^{3} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} - \frac{3 b^{3} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8 d} + \frac{b^{3} d e x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)}}{2} + \frac{3 b^{3} d e x^{2} \operatorname{acosh}{\left(c + d x \right)}}{4} - \frac{3 b^{3} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} - \frac{3 b^{3} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8} - \frac{b^{3} e \operatorname{acosh}^{3}{\left(c + d x \right)}}{4 d} - \frac{3 b^{3} e \operatorname{acosh}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c*e*x + a**3*d*e*x**2/2 + 3*a**2*b*c**2*e*acosh(c + d*x)/(2*d) + 3*a**2*b*c*e*x*acosh(c + d*x) - 3*a**2*b*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(4*d) + 3*a**2*b*d*e*x**2*acosh(c + d*x)/2 - 3*a**2*b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/4 - 3*a**2*b*e*acosh(c + d*x)/(4*d) + 3*a*b**2*c**2*e*acosh(c + d*x)**2/(2*d) + 3*a*b**2*c*e*x*acosh(c + d*x)**2 + 3*a*b**2*c*e*x/2 - 3*a*b**2*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(2*d) + 3*a*b**2*d*e*x**2*acosh(c + d*x)**2/2 + 3*a*b**2*d*e*x**2/4 - 3*a*b**2*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/2 - 3*a*b**2*e*acosh(c + d*x)**2/(4*d) + b**3*c**2*e*acosh(c + d*x)**3/(2*d) + 3*b**3*c**2*e*acosh(c + d*x)/(4*d) + b**3*c*e*x*acosh(c + d*x)**3 + 3*b**3*c*e*x*acosh(c + d*x)/2 - 3*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(4*d) - 3*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(8*d) + b**3*d*e*x**2*acosh(c + d*x)**3/2 + 3*b**3*d*e*x**2*acosh(c + d*x)/4 - 3*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/4 - 3*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/8 - b**3*e*acosh(c + d*x)**3/(4*d) - 3*b**3*e*acosh(c + d*x)/(8*d), Ne(d, 0)), (c*e*x*(a + b*acosh(c))**3, True))","A",0
117,1,282,0,0.765936," ","integrate((a+b*acosh(d*x+c))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b c \operatorname{acosh}{\left(c + d x \right)}}{d} + 3 a^{2} b x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{2} b \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} + \frac{3 a b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + 6 a b^{2} x - \frac{6 a b^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{d} + \frac{b^{3} c \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} + \frac{6 b^{3} c \operatorname{acosh}{\left(c + d x \right)}}{d} + b^{3} x \operatorname{acosh}^{3}{\left(c + d x \right)} + 6 b^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} - \frac{6 b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*c*acosh(c + d*x)/d + 3*a**2*b*x*acosh(c + d*x) - 3*a**2*b*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d + 3*a*b**2*c*acosh(c + d*x)**2/d + 3*a*b**2*x*acosh(c + d*x)**2 + 6*a*b**2*x - 6*a*b**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/d + b**3*c*acosh(c + d*x)**3/d + 6*b**3*c*acosh(c + d*x)/d + b**3*x*acosh(c + d*x)**3 + 6*b**3*x*acosh(c + d*x) - 3*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/d - 6*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d, Ne(d, 0)), (x*(a + b*acosh(c))**3, True))","A",0
118,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e),x)","\frac{\int \frac{a^{3}}{c + d x}\, dx + \int \frac{b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a^{2} b \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**3/(c + d*x), x) + Integral(b**3*acosh(c + d*x)**3/(c + d*x), x) + Integral(3*a*b**2*acosh(c + d*x)**2/(c + d*x), x) + Integral(3*a**2*b*acosh(c + d*x)/(c + d*x), x))/e","F",0
119,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{3}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a^{2} b \operatorname{acosh}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**3*acosh(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a*b**2*acosh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a**2*b*acosh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
120,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{3}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{3 a^{2} b \operatorname{acosh}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**3*acosh(c + d*x)**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(3*a*b**2*acosh(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(3*a**2*b*acosh(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
121,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{3}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{3 a^{2} b \operatorname{acosh}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**3*acosh(c + d*x)**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(3*a*b**2*acosh(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(3*a**2*b*acosh(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
122,1,2876,0,19.270678," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**4,x)","\begin{cases} a^{4} c^{3} e^{3} x + \frac{3 a^{4} c^{2} d e^{3} x^{2}}{2} + a^{4} c d^{2} e^{3} x^{3} + \frac{a^{4} d^{3} e^{3} x^{4}}{4} + \frac{a^{3} b c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{d} + 4 a^{3} b c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{a^{3} b c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4 d} + 6 a^{3} b c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{3} b c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4} + 4 a^{3} b c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{3} b c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4} - \frac{3 a^{3} b c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8 d} + a^{3} b d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)} - \frac{a^{3} b d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{4} - \frac{3 a^{3} b e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{8} - \frac{3 a^{3} b e^{3} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} c^{4} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2 d} + 6 a^{2} b^{2} c^{3} e^{3} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a^{2} b^{2} c^{3} e^{3} x}{4} - \frac{3 a^{2} b^{2} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{4 d} + 9 a^{2} b^{2} c^{2} d e^{3} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{9 a^{2} b^{2} c^{2} d e^{3} x^{2}}{8} - \frac{9 a^{2} b^{2} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{4} + 6 a^{2} b^{2} c d^{2} e^{3} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a^{2} b^{2} c d^{2} e^{3} x^{3}}{4} - \frac{9 a^{2} b^{2} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{4} + \frac{9 a^{2} b^{2} c e^{3} x}{8} - \frac{9 a^{2} b^{2} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} d^{3} e^{3} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b^{2} d^{3} e^{3} x^{4}}{16} - \frac{3 a^{2} b^{2} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{4} + \frac{9 a^{2} b^{2} d e^{3} x^{2}}{16} - \frac{9 a^{2} b^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{8} - \frac{9 a^{2} b^{2} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16 d} + \frac{a b^{3} c^{4} e^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} c^{4} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c^{3} e^{3} x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} c^{3} e^{3} x \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{3 a b^{3} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} - \frac{3 a b^{3} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32 d} + 6 a b^{3} c^{2} d e^{3} x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{9 a b^{3} c^{2} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32} + \frac{9 a b^{3} c^{2} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c d^{2} e^{3} x^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} c d^{2} e^{3} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{9 a b^{3} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32} + \frac{9 a b^{3} c e^{3} x \operatorname{acosh}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{8 d} - \frac{45 a b^{3} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{64 d} + a b^{3} d^{3} e^{3} x^{4} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{3 a b^{3} d^{3} e^{3} x^{4} \operatorname{acosh}{\left(c + d x \right)}}{8} - \frac{3 a b^{3} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} - \frac{3 a b^{3} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{32} + \frac{9 a b^{3} d e^{3} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{8} - \frac{9 a b^{3} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{8} - \frac{45 a b^{3} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{64} - \frac{3 a b^{3} e^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{8 d} - \frac{45 a b^{3} e^{3} \operatorname{acosh}{\left(c + d x \right)}}{64 d} + \frac{b^{4} c^{4} e^{3} \operatorname{acosh}^{4}{\left(c + d x \right)}}{4 d} + \frac{3 b^{4} c^{4} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c^{3} e^{3} x \operatorname{acosh}^{4}{\left(c + d x \right)} + \frac{3 b^{4} c^{3} e^{3} x \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} c^{3} e^{3} x}{32} - \frac{b^{4} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4 d} - \frac{3 b^{4} c^{3} e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{32 d} + \frac{3 b^{4} c^{2} d e^{3} x^{2} \operatorname{acosh}^{4}{\left(c + d x \right)}}{2} + \frac{9 b^{4} c^{2} d e^{3} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{8} + \frac{9 b^{4} c^{2} d e^{3} x^{2}}{64} - \frac{3 b^{4} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4} - \frac{9 b^{4} c^{2} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{32} + \frac{9 b^{4} c^{2} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c d^{2} e^{3} x^{3} \operatorname{acosh}^{4}{\left(c + d x \right)} + \frac{3 b^{4} c d^{2} e^{3} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} c d^{2} e^{3} x^{3}}{32} - \frac{3 b^{4} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4} - \frac{9 b^{4} c d e^{3} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{32} + \frac{9 b^{4} c e^{3} x \operatorname{acosh}^{2}{\left(c + d x \right)}}{8} + \frac{45 b^{4} c e^{3} x}{64} - \frac{3 b^{4} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{8 d} - \frac{45 b^{4} c e^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{64 d} + \frac{b^{4} d^{3} e^{3} x^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}{4} + \frac{3 b^{4} d^{3} e^{3} x^{4} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{4} d^{3} e^{3} x^{4}}{128} - \frac{b^{4} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{4} - \frac{3 b^{4} d^{2} e^{3} x^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{32} + \frac{9 b^{4} d e^{3} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{16} + \frac{45 b^{4} d e^{3} x^{2}}{128} - \frac{3 b^{4} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{8} - \frac{45 b^{4} e^{3} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{64} - \frac{3 b^{4} e^{3} \operatorname{acosh}^{4}{\left(c + d x \right)}}{32 d} - \frac{45 b^{4} e^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**3*e**3*x + 3*a**4*c**2*d*e**3*x**2/2 + a**4*c*d**2*e**3*x**3 + a**4*d**3*e**3*x**4/4 + a**3*b*c**4*e**3*acosh(c + d*x)/d + 4*a**3*b*c**3*e**3*x*acosh(c + d*x) - a**3*b*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(4*d) + 6*a**3*b*c**2*d*e**3*x**2*acosh(c + d*x) - 3*a**3*b*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/4 + 4*a**3*b*c*d**2*e**3*x**3*acosh(c + d*x) - 3*a**3*b*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/4 - 3*a**3*b*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(8*d) + a**3*b*d**3*e**3*x**4*acosh(c + d*x) - a**3*b*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/4 - 3*a**3*b*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/8 - 3*a**3*b*e**3*acosh(c + d*x)/(8*d) + 3*a**2*b**2*c**4*e**3*acosh(c + d*x)**2/(2*d) + 6*a**2*b**2*c**3*e**3*x*acosh(c + d*x)**2 + 3*a**2*b**2*c**3*e**3*x/4 - 3*a**2*b**2*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(4*d) + 9*a**2*b**2*c**2*d*e**3*x**2*acosh(c + d*x)**2 + 9*a**2*b**2*c**2*d*e**3*x**2/8 - 9*a**2*b**2*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/4 + 6*a**2*b**2*c*d**2*e**3*x**3*acosh(c + d*x)**2 + 3*a**2*b**2*c*d**2*e**3*x**3/4 - 9*a**2*b**2*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/4 + 9*a**2*b**2*c*e**3*x/8 - 9*a**2*b**2*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(8*d) + 3*a**2*b**2*d**3*e**3*x**4*acosh(c + d*x)**2/2 + 3*a**2*b**2*d**3*e**3*x**4/16 - 3*a**2*b**2*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/4 + 9*a**2*b**2*d*e**3*x**2/16 - 9*a**2*b**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/8 - 9*a**2*b**2*e**3*acosh(c + d*x)**2/(16*d) + a*b**3*c**4*e**3*acosh(c + d*x)**3/d + 3*a*b**3*c**4*e**3*acosh(c + d*x)/(8*d) + 4*a*b**3*c**3*e**3*x*acosh(c + d*x)**3 + 3*a*b**3*c**3*e**3*x*acosh(c + d*x)/2 - 3*a*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(4*d) - 3*a*b**3*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(32*d) + 6*a*b**3*c**2*d*e**3*x**2*acosh(c + d*x)**3 + 9*a*b**3*c**2*d*e**3*x**2*acosh(c + d*x)/4 - 9*a*b**3*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/4 - 9*a*b**3*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/32 + 9*a*b**3*c**2*e**3*acosh(c + d*x)/(8*d) + 4*a*b**3*c*d**2*e**3*x**3*acosh(c + d*x)**3 + 3*a*b**3*c*d**2*e**3*x**3*acosh(c + d*x)/2 - 9*a*b**3*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/4 - 9*a*b**3*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/32 + 9*a*b**3*c*e**3*x*acosh(c + d*x)/4 - 9*a*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(8*d) - 45*a*b**3*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(64*d) + a*b**3*d**3*e**3*x**4*acosh(c + d*x)**3 + 3*a*b**3*d**3*e**3*x**4*acosh(c + d*x)/8 - 3*a*b**3*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/4 - 3*a*b**3*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/32 + 9*a*b**3*d*e**3*x**2*acosh(c + d*x)/8 - 9*a*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/8 - 45*a*b**3*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/64 - 3*a*b**3*e**3*acosh(c + d*x)**3/(8*d) - 45*a*b**3*e**3*acosh(c + d*x)/(64*d) + b**4*c**4*e**3*acosh(c + d*x)**4/(4*d) + 3*b**4*c**4*e**3*acosh(c + d*x)**2/(16*d) + b**4*c**3*e**3*x*acosh(c + d*x)**4 + 3*b**4*c**3*e**3*x*acosh(c + d*x)**2/4 + 3*b**4*c**3*e**3*x/32 - b**4*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/(4*d) - 3*b**4*c**3*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(32*d) + 3*b**4*c**2*d*e**3*x**2*acosh(c + d*x)**4/2 + 9*b**4*c**2*d*e**3*x**2*acosh(c + d*x)**2/8 + 9*b**4*c**2*d*e**3*x**2/64 - 3*b**4*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/4 - 9*b**4*c**2*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/32 + 9*b**4*c**2*e**3*acosh(c + d*x)**2/(16*d) + b**4*c*d**2*e**3*x**3*acosh(c + d*x)**4 + 3*b**4*c*d**2*e**3*x**3*acosh(c + d*x)**2/4 + 3*b**4*c*d**2*e**3*x**3/32 - 3*b**4*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/4 - 9*b**4*c*d*e**3*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/32 + 9*b**4*c*e**3*x*acosh(c + d*x)**2/8 + 45*b**4*c*e**3*x/64 - 3*b**4*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/(8*d) - 45*b**4*c*e**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(64*d) + b**4*d**3*e**3*x**4*acosh(c + d*x)**4/4 + 3*b**4*d**3*e**3*x**4*acosh(c + d*x)**2/16 + 3*b**4*d**3*e**3*x**4/128 - b**4*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/4 - 3*b**4*d**2*e**3*x**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/32 + 9*b**4*d*e**3*x**2*acosh(c + d*x)**2/16 + 45*b**4*d*e**3*x**2/128 - 3*b**4*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/8 - 45*b**4*e**3*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/64 - 3*b**4*e**3*acosh(c + d*x)**4/(32*d) - 45*b**4*e**3*acosh(c + d*x)**2/(128*d), Ne(d, 0)), (c**3*e**3*x*(a + b*acosh(c))**4, True))","A",0
123,1,1889,0,9.094051," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**4,x)","\begin{cases} a^{4} c^{2} e^{2} x + a^{4} c d e^{2} x^{2} + \frac{a^{4} d^{2} e^{2} x^{3}}{3} + \frac{4 a^{3} b c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + 4 a^{3} b c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)} - \frac{4 a^{3} b c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} + 4 a^{3} b c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)} - \frac{8 a^{3} b c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} + \frac{4 a^{3} b d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{4 a^{3} b d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9} - \frac{8 a^{3} b e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{9 d} + \frac{2 a^{2} b^{2} c^{3} e^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c^{2} e^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{4 a^{2} b^{2} c^{2} e^{2} x}{3} - \frac{4 a^{2} b^{2} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + 6 a^{2} b^{2} c d e^{2} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{4 a^{2} b^{2} c d e^{2} x^{2}}{3} - \frac{8 a^{2} b^{2} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3} + 2 a^{2} b^{2} d^{2} e^{2} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{4 a^{2} b^{2} d^{2} e^{2} x^{3}}{9} - \frac{4 a^{2} b^{2} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3} + \frac{8 a^{2} b^{2} e^{2} x}{3} - \frac{8 a^{2} b^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} c^{3} e^{2} \operatorname{acosh}^{3}{\left(c + d x \right)}}{3 d} + \frac{8 a b^{3} c^{3} e^{2} \operatorname{acosh}{\left(c + d x \right)}}{9 d} + 4 a b^{3} c^{2} e^{2} x \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{8 a b^{3} c^{2} e^{2} x \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{4 a b^{3} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} - \frac{8 a b^{3} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27 d} + 4 a b^{3} c d e^{2} x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)} + \frac{8 a b^{3} c d e^{2} x^{2} \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{8 a b^{3} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} - \frac{16 a b^{3} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27} + \frac{16 a b^{3} c e^{2} \operatorname{acosh}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} d^{2} e^{2} x^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{3} + \frac{8 a b^{3} d^{2} e^{2} x^{3} \operatorname{acosh}{\left(c + d x \right)}}{9} - \frac{4 a b^{3} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} - \frac{8 a b^{3} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27} + \frac{16 a b^{3} e^{2} x \operatorname{acosh}{\left(c + d x \right)}}{3} - \frac{8 a b^{3} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} - \frac{160 a b^{3} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{27 d} + \frac{b^{4} c^{3} e^{2} \operatorname{acosh}^{4}{\left(c + d x \right)}}{3 d} + \frac{4 b^{4} c^{3} e^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{9 d} + b^{4} c^{2} e^{2} x \operatorname{acosh}^{4}{\left(c + d x \right)} + \frac{4 b^{4} c^{2} e^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} + \frac{8 b^{4} c^{2} e^{2} x}{27} - \frac{4 b^{4} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{9 d} - \frac{8 b^{4} c^{2} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{27 d} + b^{4} c d e^{2} x^{2} \operatorname{acosh}^{4}{\left(c + d x \right)} + \frac{4 b^{4} c d e^{2} x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} + \frac{8 b^{4} c d e^{2} x^{2}}{27} - \frac{8 b^{4} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{9} - \frac{16 b^{4} c e^{2} x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{27} + \frac{8 b^{4} c e^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{4} d^{2} e^{2} x^{3} \operatorname{acosh}^{4}{\left(c + d x \right)}}{3} + \frac{4 b^{4} d^{2} e^{2} x^{3} \operatorname{acosh}^{2}{\left(c + d x \right)}}{9} + \frac{8 b^{4} d^{2} e^{2} x^{3}}{81} - \frac{4 b^{4} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{9} - \frac{8 b^{4} d e^{2} x^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{27} + \frac{8 b^{4} e^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)}}{3} + \frac{160 b^{4} e^{2} x}{27} - \frac{8 b^{4} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{9 d} - \frac{160 b^{4} e^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{27 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*e**2*x + a**4*c*d*e**2*x**2 + a**4*d**2*e**2*x**3/3 + 4*a**3*b*c**3*e**2*acosh(c + d*x)/(3*d) + 4*a**3*b*c**2*e**2*x*acosh(c + d*x) - 4*a**3*b*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d) + 4*a**3*b*c*d*e**2*x**2*acosh(c + d*x) - 8*a**3*b*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 + 4*a**3*b*d**2*e**2*x**3*acosh(c + d*x)/3 - 4*a**3*b*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/9 - 8*a**3*b*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(9*d) + 2*a**2*b**2*c**3*e**2*acosh(c + d*x)**2/d + 6*a**2*b**2*c**2*e**2*x*acosh(c + d*x)**2 + 4*a**2*b**2*c**2*e**2*x/3 - 4*a**2*b**2*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(3*d) + 6*a**2*b**2*c*d*e**2*x**2*acosh(c + d*x)**2 + 4*a**2*b**2*c*d*e**2*x**2/3 - 8*a**2*b**2*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/3 + 2*a**2*b**2*d**2*e**2*x**3*acosh(c + d*x)**2 + 4*a**2*b**2*d**2*e**2*x**3/9 - 4*a**2*b**2*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/3 + 8*a**2*b**2*e**2*x/3 - 8*a**2*b**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(3*d) + 4*a*b**3*c**3*e**2*acosh(c + d*x)**3/(3*d) + 8*a*b**3*c**3*e**2*acosh(c + d*x)/(9*d) + 4*a*b**3*c**2*e**2*x*acosh(c + d*x)**3 + 8*a*b**3*c**2*e**2*x*acosh(c + d*x)/3 - 4*a*b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(3*d) - 8*a*b**3*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(27*d) + 4*a*b**3*c*d*e**2*x**2*acosh(c + d*x)**3 + 8*a*b**3*c*d*e**2*x**2*acosh(c + d*x)/3 - 8*a*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/3 - 16*a*b**3*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/27 + 16*a*b**3*c*e**2*acosh(c + d*x)/(3*d) + 4*a*b**3*d**2*e**2*x**3*acosh(c + d*x)**3/3 + 8*a*b**3*d**2*e**2*x**3*acosh(c + d*x)/9 - 4*a*b**3*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/3 - 8*a*b**3*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/27 + 16*a*b**3*e**2*x*acosh(c + d*x)/3 - 8*a*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/(3*d) - 160*a*b**3*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(27*d) + b**4*c**3*e**2*acosh(c + d*x)**4/(3*d) + 4*b**4*c**3*e**2*acosh(c + d*x)**2/(9*d) + b**4*c**2*e**2*x*acosh(c + d*x)**4 + 4*b**4*c**2*e**2*x*acosh(c + d*x)**2/3 + 8*b**4*c**2*e**2*x/27 - 4*b**4*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/(9*d) - 8*b**4*c**2*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(27*d) + b**4*c*d*e**2*x**2*acosh(c + d*x)**4 + 4*b**4*c*d*e**2*x**2*acosh(c + d*x)**2/3 + 8*b**4*c*d*e**2*x**2/27 - 8*b**4*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/9 - 16*b**4*c*e**2*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/27 + 8*b**4*c*e**2*acosh(c + d*x)**2/(3*d) + b**4*d**2*e**2*x**3*acosh(c + d*x)**4/3 + 4*b**4*d**2*e**2*x**3*acosh(c + d*x)**2/9 + 8*b**4*d**2*e**2*x**3/81 - 4*b**4*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/9 - 8*b**4*d*e**2*x**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/27 + 8*b**4*e**2*x*acosh(c + d*x)**2/3 + 160*b**4*e**2*x/27 - 8*b**4*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/(9*d) - 160*b**4*e**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(27*d), Ne(d, 0)), (c**2*e**2*x*(a + b*acosh(c))**4, True))","A",0
124,1,1027,0,4.516383," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**4,x)","\begin{cases} a^{4} c e x + \frac{a^{4} d e x^{2}}{2} + \frac{2 a^{3} b c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{d} + 4 a^{3} b c e x \operatorname{acosh}{\left(c + d x \right)} - \frac{a^{3} b c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} + 2 a^{3} b d e x^{2} \operatorname{acosh}{\left(c + d x \right)} - a^{3} b e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} - \frac{a^{3} b e \operatorname{acosh}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} c^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c e x \operatorname{acosh}^{2}{\left(c + d x \right)} + 3 a^{2} b^{2} c e x - \frac{3 a^{2} b^{2} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{d} + 3 a^{2} b^{2} d e x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 a^{2} b^{2} d e x^{2}}{2} - 3 a^{2} b^{2} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a^{2} b^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{2 d} + \frac{2 a b^{3} c^{2} e \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} c^{2} e \operatorname{acosh}{\left(c + d x \right)}}{d} + 4 a b^{3} c e x \operatorname{acosh}^{3}{\left(c + d x \right)} + 6 a b^{3} c e x \operatorname{acosh}{\left(c + d x \right)} - \frac{3 a b^{3} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} - \frac{3 a b^{3} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{2 d} + 2 a b^{3} d e x^{2} \operatorname{acosh}^{3}{\left(c + d x \right)} + 3 a b^{3} d e x^{2} \operatorname{acosh}{\left(c + d x \right)} - 3 a b^{3} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)} - \frac{3 a b^{3} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{2} - \frac{a b^{3} e \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} - \frac{3 a b^{3} e \operatorname{acosh}{\left(c + d x \right)}}{2 d} + \frac{b^{4} c^{2} e \operatorname{acosh}^{4}{\left(c + d x \right)}}{2 d} + \frac{3 b^{4} c^{2} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{2 d} + b^{4} c e x \operatorname{acosh}^{4}{\left(c + d x \right)} + 3 b^{4} c e x \operatorname{acosh}^{2}{\left(c + d x \right)} + \frac{3 b^{4} c e x}{2} - \frac{b^{4} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} - \frac{3 b^{4} c e \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2 d} + \frac{b^{4} d e x^{2} \operatorname{acosh}^{4}{\left(c + d x \right)}}{2} + \frac{3 b^{4} d e x^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{2} + \frac{3 b^{4} d e x^{2}}{4} - b^{4} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)} - \frac{3 b^{4} e x \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{2} - \frac{b^{4} e \operatorname{acosh}^{4}{\left(c + d x \right)}}{4 d} - \frac{3 b^{4} e \operatorname{acosh}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c*e*x + a**4*d*e*x**2/2 + 2*a**3*b*c**2*e*acosh(c + d*x)/d + 4*a**3*b*c*e*x*acosh(c + d*x) - a**3*b*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d + 2*a**3*b*d*e*x**2*acosh(c + d*x) - a**3*b*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1) - a**3*b*e*acosh(c + d*x)/d + 3*a**2*b**2*c**2*e*acosh(c + d*x)**2/d + 6*a**2*b**2*c*e*x*acosh(c + d*x)**2 + 3*a**2*b**2*c*e*x - 3*a**2*b**2*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/d + 3*a**2*b**2*d*e*x**2*acosh(c + d*x)**2 + 3*a**2*b**2*d*e*x**2/2 - 3*a**2*b**2*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x) - 3*a**2*b**2*e*acosh(c + d*x)**2/(2*d) + 2*a*b**3*c**2*e*acosh(c + d*x)**3/d + 3*a*b**3*c**2*e*acosh(c + d*x)/d + 4*a*b**3*c*e*x*acosh(c + d*x)**3 + 6*a*b**3*c*e*x*acosh(c + d*x) - 3*a*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/d - 3*a*b**3*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/(2*d) + 2*a*b**3*d*e*x**2*acosh(c + d*x)**3 + 3*a*b**3*d*e*x**2*acosh(c + d*x) - 3*a*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2 - 3*a*b**3*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/2 - a*b**3*e*acosh(c + d*x)**3/d - 3*a*b**3*e*acosh(c + d*x)/(2*d) + b**4*c**2*e*acosh(c + d*x)**4/(2*d) + 3*b**4*c**2*e*acosh(c + d*x)**2/(2*d) + b**4*c*e*x*acosh(c + d*x)**4 + 3*b**4*c*e*x*acosh(c + d*x)**2 + 3*b**4*c*e*x/2 - b**4*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/d - 3*b**4*c*e*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/(2*d) + b**4*d*e*x**2*acosh(c + d*x)**4/2 + 3*b**4*d*e*x**2*acosh(c + d*x)**2/2 + 3*b**4*d*e*x**2/4 - b**4*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3 - 3*b**4*e*x*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/2 - b**4*e*acosh(c + d*x)**4/(4*d) - 3*b**4*e*acosh(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*acosh(c))**4, True))","A",0
125,1,444,0,1.598452," ","integrate((a+b*acosh(d*x+c))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b c \operatorname{acosh}{\left(c + d x \right)}}{d} + 4 a^{3} b x \operatorname{acosh}{\left(c + d x \right)} - \frac{4 a^{3} b \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} + \frac{6 a^{2} b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} x \operatorname{acosh}^{2}{\left(c + d x \right)} + 12 a^{2} b^{2} x - \frac{12 a^{2} b^{2} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{d} + \frac{4 a b^{3} c \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} + \frac{24 a b^{3} c \operatorname{acosh}{\left(c + d x \right)}}{d} + 4 a b^{3} x \operatorname{acosh}^{3}{\left(c + d x \right)} + 24 a b^{3} x \operatorname{acosh}{\left(c + d x \right)} - \frac{12 a b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} - \frac{24 a b^{3} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1}}{d} + \frac{b^{4} c \operatorname{acosh}^{4}{\left(c + d x \right)}}{d} + \frac{12 b^{4} c \operatorname{acosh}^{2}{\left(c + d x \right)}}{d} + b^{4} x \operatorname{acosh}^{4}{\left(c + d x \right)} + 12 b^{4} x \operatorname{acosh}^{2}{\left(c + d x \right)} + 24 b^{4} x - \frac{4 b^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}^{3}{\left(c + d x \right)}}{d} - \frac{24 b^{4} \sqrt{c^{2} + 2 c d x + d^{2} x^{2} - 1} \operatorname{acosh}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{acosh}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*c*acosh(c + d*x)/d + 4*a**3*b*x*acosh(c + d*x) - 4*a**3*b*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d + 6*a**2*b**2*c*acosh(c + d*x)**2/d + 6*a**2*b**2*x*acosh(c + d*x)**2 + 12*a**2*b**2*x - 12*a**2*b**2*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/d + 4*a*b**3*c*acosh(c + d*x)**3/d + 24*a*b**3*c*acosh(c + d*x)/d + 4*a*b**3*x*acosh(c + d*x)**3 + 24*a*b**3*x*acosh(c + d*x) - 12*a*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**2/d - 24*a*b**3*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)/d + b**4*c*acosh(c + d*x)**4/d + 12*b**4*c*acosh(c + d*x)**2/d + b**4*x*acosh(c + d*x)**4 + 12*b**4*x*acosh(c + d*x)**2 + 24*b**4*x - 4*b**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)**3/d - 24*b**4*sqrt(c**2 + 2*c*d*x + d**2*x**2 - 1)*acosh(c + d*x)/d, Ne(d, 0)), (x*(a + b*acosh(c))**4, True))","A",0
126,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e),x)","\frac{\int \frac{a^{4}}{c + d x}\, dx + \int \frac{b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a^{3} b \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**4/(c + d*x), x) + Integral(b**4*acosh(c + d*x)**4/(c + d*x), x) + Integral(4*a*b**3*acosh(c + d*x)**3/(c + d*x), x) + Integral(6*a**2*b**2*acosh(c + d*x)**2/(c + d*x), x) + Integral(4*a**3*b*acosh(c + d*x)/(c + d*x), x))/e","F",0
127,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{4}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a^{3} b \operatorname{acosh}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**4/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**4*acosh(c + d*x)**4/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a*b**3*acosh(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(6*a**2*b**2*acosh(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a**3*b*acosh(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
128,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{4}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{4 a^{3} b \operatorname{acosh}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**4/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**4*acosh(c + d*x)**4/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(4*a*b**3*acosh(c + d*x)**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(6*a**2*b**2*acosh(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(4*a**3*b*acosh(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
129,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{4}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{4 a^{3} b \operatorname{acosh}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**4/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**4*acosh(c + d*x)**4/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(4*a*b**3*acosh(c + d*x)**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(6*a**2*b**2*acosh(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(4*a**3*b*acosh(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
130,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c)),x)","e^{4} \left(\int \frac{c^{4}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a + b*acosh(c + d*x)), x) + Integral(d**4*x**4/(a + b*acosh(c + d*x)), x) + Integral(4*c*d**3*x**3/(a + b*acosh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a + b*acosh(c + d*x)), x) + Integral(4*c**3*d*x/(a + b*acosh(c + d*x)), x))","F",0
131,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c)),x)","e^{3} \left(\int \frac{c^{3}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a + b*acosh(c + d*x)), x) + Integral(d**3*x**3/(a + b*acosh(c + d*x)), x) + Integral(3*c*d**2*x**2/(a + b*acosh(c + d*x)), x) + Integral(3*c**2*d*x/(a + b*acosh(c + d*x)), x))","F",0
132,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c)),x)","e^{2} \left(\int \frac{c^{2}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a + b*acosh(c + d*x)), x) + Integral(d**2*x**2/(a + b*acosh(c + d*x)), x) + Integral(2*c*d*x/(a + b*acosh(c + d*x)), x))","F",0
133,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c)),x)","e \left(\int \frac{c}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a + b*acosh(c + d*x)), x) + Integral(d*x/(a + b*acosh(c + d*x)), x))","F",0
134,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c)),x)","\int \frac{1}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*acosh(c + d*x)), x)","F",0
135,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c)),x)","\frac{\int \frac{1}{a c + a d x + b c \operatorname{acosh}{\left(c + d x \right)} + b d x \operatorname{acosh}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c + a*d*x + b*c*acosh(c + d*x) + b*d*x*acosh(c + d*x)), x)/e","F",0
136,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**2,x)","e^{4} \left(\int \frac{c^{4}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(d**4*x**4/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(4*c*d**3*x**3/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(6*c**2*d**2*x**2/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(4*c**3*d*x/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x))","F",0
137,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**2,x)","e^{3} \left(\int \frac{c^{3}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(d**3*x**3/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x))","F",0
138,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**2,x)","e^{2} \left(\int \frac{c^{2}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(d**2*x**2/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(2*c*d*x/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x))","F",0
139,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**2,x)","e \left(\int \frac{c}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} + 2 a b \operatorname{acosh}{\left(c + d x \right)} + b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x) + Integral(d*x/(a**2 + 2*a*b*acosh(c + d*x) + b**2*acosh(c + d*x)**2), x))","F",0
140,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**2,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-2), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**2,x)","\frac{\int \frac{1}{a^{2} c + a^{2} d x + 2 a b c \operatorname{acosh}{\left(c + d x \right)} + 2 a b d x \operatorname{acosh}{\left(c + d x \right)} + b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{2} d x \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c + a**2*d*x + 2*a*b*c*acosh(c + d*x) + 2*a*b*d*x*acosh(c + d*x) + b**2*c*acosh(c + d*x)**2 + b**2*d*x*acosh(c + d*x)**2), x)/e","F",0
142,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**3,x)","e^{4} \left(\int \frac{c^{4}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(d**4*x**4/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(4*c*d**3*x**3/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(6*c**2*d**2*x**2/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(4*c**3*d*x/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x))","F",0
143,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**3,x)","e^{3} \left(\int \frac{c^{3}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(d**3*x**3/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x))","F",0
144,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**3,x)","e^{2} \left(\int \frac{c^{2}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(d**2*x**2/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(2*c*d*x/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x))","F",0
145,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**3,x)","e \left(\int \frac{c}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{3} + 3 a^{2} b \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x) + Integral(d*x/(a**3 + 3*a**2*b*acosh(c + d*x) + 3*a*b**2*acosh(c + d*x)**2 + b**3*acosh(c + d*x)**3), x))","F",0
146,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**3,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-3), x)","F",0
147,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**3,x)","\frac{\int \frac{1}{a^{3} c + a^{3} d x + 3 a^{2} b c \operatorname{acosh}{\left(c + d x \right)} + 3 a^{2} b d x \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)} + 3 a b^{2} d x \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} c \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{3} d x \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**3*c + a**3*d*x + 3*a**2*b*c*acosh(c + d*x) + 3*a**2*b*d*x*acosh(c + d*x) + 3*a*b**2*c*acosh(c + d*x)**2 + 3*a*b**2*d*x*acosh(c + d*x)**2 + b**3*c*acosh(c + d*x)**3 + b**3*d*x*acosh(c + d*x)**3), x)/e","F",0
148,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**4,x)","e^{4} \left(\int \frac{c^{4}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(d**4*x**4/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(4*c*d**3*x**3/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(6*c**2*d**2*x**2/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(4*c**3*d*x/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x))","F",0
149,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**4,x)","e^{3} \left(\int \frac{c^{3}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(d**3*x**3/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(3*c*d**2*x**2/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(3*c**2*d*x/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x))","F",0
150,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**4,x)","e^{2} \left(\int \frac{c^{2}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(d**2*x**2/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(2*c*d*x/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x))","F",0
151,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**4,x)","e \left(\int \frac{c}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{4} + 4 a^{3} b \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x) + Integral(d*x/(a**4 + 4*a**3*b*acosh(c + d*x) + 6*a**2*b**2*acosh(c + d*x)**2 + 4*a*b**3*acosh(c + d*x)**3 + b**4*acosh(c + d*x)**4), x))","F",0
152,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**4,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-4), x)","F",0
153,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**4,x)","\frac{\int \frac{1}{a^{4} c + a^{4} d x + 4 a^{3} b c \operatorname{acosh}{\left(c + d x \right)} + 4 a^{3} b d x \operatorname{acosh}{\left(c + d x \right)} + 6 a^{2} b^{2} c \operatorname{acosh}^{2}{\left(c + d x \right)} + 6 a^{2} b^{2} d x \operatorname{acosh}^{2}{\left(c + d x \right)} + 4 a b^{3} c \operatorname{acosh}^{3}{\left(c + d x \right)} + 4 a b^{3} d x \operatorname{acosh}^{3}{\left(c + d x \right)} + b^{4} c \operatorname{acosh}^{4}{\left(c + d x \right)} + b^{4} d x \operatorname{acosh}^{4}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**4*c + a**4*d*x + 4*a**3*b*c*acosh(c + d*x) + 4*a**3*b*d*x*acosh(c + d*x) + 6*a**2*b**2*c*acosh(c + d*x)**2 + 6*a**2*b**2*d*x*acosh(c + d*x)**2 + 4*a*b**3*c*acosh(c + d*x)**3 + 4*a*b**3*d*x*acosh(c + d*x)**3 + b**4*c*acosh(c + d*x)**4 + b**4*d*x*acosh(c + d*x)**4), x)/e","F",0
154,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4*(a+b*acosh(d*x+c))**(1/2),x)","e^{4} \left(\int c^{4} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int d^{4} x^{4} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 4 c d^{3} x^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 6 c^{2} d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 4 c^{3} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4*sqrt(a + b*acosh(c + d*x)), x) + Integral(d**4*x**4*sqrt(a + b*acosh(c + d*x)), x) + Integral(4*c*d**3*x**3*sqrt(a + b*acosh(c + d*x)), x) + Integral(6*c**2*d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(4*c**3*d*x*sqrt(a + b*acosh(c + d*x)), x))","F",0
155,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**(1/2),x)","e^{3} \left(\int c^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int d^{3} x^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 3 c d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 3 c^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3*sqrt(a + b*acosh(c + d*x)), x) + Integral(d**3*x**3*sqrt(a + b*acosh(c + d*x)), x) + Integral(3*c*d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(3*c**2*d*x*sqrt(a + b*acosh(c + d*x)), x))","F",0
156,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**(1/2),x)","e^{2} \left(\int c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 2 c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(2*c*d*x*sqrt(a + b*acosh(c + d*x)), x))","F",0
157,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**(1/2),x)","e \left(\int c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c*sqrt(a + b*acosh(c + d*x)), x) + Integral(d*x*sqrt(a + b*acosh(c + d*x)), x))","F",0
158,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(1/2),x)","\int \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*acosh(c + d*x)), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(1/2)/(d*e*x+c*e),x)","\frac{\int \frac{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}{c + d x}\, dx}{e}"," ",0,"Integral(sqrt(a + b*acosh(c + d*x))/(c + d*x), x)/e","F",0
160,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**(3/2),x)","e^{3} \left(\int a c^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int a d^{3} x^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b c^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 3 a c d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int 3 a c^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b d^{3} x^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 3 b c d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 3 b c^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**3*(Integral(a*c**3*sqrt(a + b*acosh(c + d*x)), x) + Integral(a*d**3*x**3*sqrt(a + b*acosh(c + d*x)), x) + Integral(b*c**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(3*a*c*d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(3*a*c**2*d*x*sqrt(a + b*acosh(c + d*x)), x) + Integral(b*d**3*x**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(3*b*c*d**2*x**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(3*b*c**2*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x))","F",0
161,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**(3/2),x)","e^{2} \left(\int a c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int a d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 2 a c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 2 b c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a*c**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(a*d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(b*c**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(2*a*c*d*x*sqrt(a + b*acosh(c + d*x)), x) + Integral(b*d**2*x**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(2*b*c*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x))","F",0
162,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**(3/2),x)","e \left(\int a c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int a d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int b d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a*c*sqrt(a + b*acosh(c + d*x)), x) + Integral(a*d*x*sqrt(a + b*acosh(c + d*x)), x) + Integral(b*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(b*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x))","F",0
163,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(3/2),x)","\int \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(3/2), x)","F",0
164,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(3/2)/(d*e*x+c*e),x)","\frac{\int \frac{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a*sqrt(a + b*acosh(c + d*x))/(c + d*x), x) + Integral(b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)/(c + d*x), x))/e","F",0
165,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*acosh(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**(5/2),x)","e^{2} \left(\int a^{2} c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int a^{2} d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b^{2} c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 2 a^{2} c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b^{2} d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d^{2} x^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int 2 b^{2} c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}\, dx + \int 4 a b c d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a**2*c**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(a**2*d**2*x**2*sqrt(a + b*acosh(c + d*x)), x) + Integral(b**2*c**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2, x) + Integral(2*a*b*c**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(2*a**2*c*d*x*sqrt(a + b*acosh(c + d*x)), x) + Integral(b**2*d**2*x**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2, x) + Integral(2*a*b*d**2*x**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(2*b**2*c*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2, x) + Integral(4*a*b*c*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x))","F",0
167,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**(5/2),x)","e \left(\int a^{2} c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int a^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int b^{2} c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx + \int b^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a**2*c*sqrt(a + b*acosh(c + d*x)), x) + Integral(a**2*d*x*sqrt(a + b*acosh(c + d*x)), x) + Integral(b**2*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2, x) + Integral(2*a*b*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x) + Integral(b**2*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2, x) + Integral(2*a*b*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x), x))","F",0
168,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(5/2),x)","\int \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(5/2)/(d*e*x+c*e),x)","\frac{\int \frac{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2*sqrt(a + b*acosh(c + d*x))/(c + d*x), x) + Integral(b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)/(c + d*x), x))/e","F",0
170,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*acosh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*acosh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**(7/2)/(d*e*x+c*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**(1/2),x)","e^{4} \left(\int \frac{c^{4}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{4} x^{4}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{4 c d^{3} x^{3}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{4 c^{3} d x}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**4*(Integral(c**4/sqrt(a + b*acosh(c + d*x)), x) + Integral(d**4*x**4/sqrt(a + b*acosh(c + d*x)), x) + Integral(4*c*d**3*x**3/sqrt(a + b*acosh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/sqrt(a + b*acosh(c + d*x)), x) + Integral(4*c**3*d*x/sqrt(a + b*acosh(c + d*x)), x))","F",0
175,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**(1/2),x)","e^{3} \left(\int \frac{c^{3}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{3} x^{3}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{3 c d^{2} x^{2}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{3 c^{2} d x}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**3*(Integral(c**3/sqrt(a + b*acosh(c + d*x)), x) + Integral(d**3*x**3/sqrt(a + b*acosh(c + d*x)), x) + Integral(3*c*d**2*x**2/sqrt(a + b*acosh(c + d*x)), x) + Integral(3*c**2*d*x/sqrt(a + b*acosh(c + d*x)), x))","F",0
176,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**(1/2),x)","e^{2} \left(\int \frac{c^{2}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{d^{2} x^{2}}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{2 c d x}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**2*(Integral(c**2/sqrt(a + b*acosh(c + d*x)), x) + Integral(d**2*x**2/sqrt(a + b*acosh(c + d*x)), x) + Integral(2*c*d*x/sqrt(a + b*acosh(c + d*x)), x))","F",0
177,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**(1/2),x)","e \left(\int \frac{c}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx + \int \frac{d x}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e*(Integral(c/sqrt(a + b*acosh(c + d*x)), x) + Integral(d*x/sqrt(a + b*acosh(c + d*x)), x))","F",0
178,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*acosh(c + d*x)), x)","F",0
179,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**(1/2),x)","\frac{\int \frac{1}{c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}}}\, dx}{e}"," ",0,"Integral(1/(c*sqrt(a + b*acosh(c + d*x)) + d*x*sqrt(a + b*acosh(c + d*x))), x)/e","F",0
180,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**(3/2),x)","e^{4} \left(\int \frac{c^{4}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(d**4*x**4/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(4*c*d**3*x**3/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(4*c**3*d*x/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x))","F",0
181,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**(3/2),x)","e^{3} \left(\int \frac{c^{3}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(d**3*x**3/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(3*c*d**2*x**2/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(3*c**2*d*x/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x))","F",0
182,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**(3/2),x)","e^{2} \left(\int \frac{c^{2}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(d**2*x**2/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(2*c*d*x/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x))","F",0
183,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**(3/2),x)","e \left(\int \frac{c}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x) + Integral(d*x/(a*sqrt(a + b*acosh(c + d*x)) + b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x))","F",0
184,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-3/2), x)","F",0
185,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**(3/2),x)","\frac{\int \frac{1}{a c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + a d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + b c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c*sqrt(a + b*acosh(c + d*x)) + a*d*x*sqrt(a + b*acosh(c + d*x)) + b*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)), x)/e","F",0
186,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**(5/2),x)","e^{4} \left(\int \frac{c^{4}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(d**4*x**4/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(4*c*d**3*x**3/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(6*c**2*d**2*x**2/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(4*c**3*d*x/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x))","F",0
187,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**(5/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(d**3*x**3/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x))","F",0
188,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**(5/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(d**2*x**2/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(2*c*d*x/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x))","F",0
189,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**(5/2),x)","e \left(\int \frac{c}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x) + Integral(d*x/(a**2*sqrt(a + b*acosh(c + d*x)) + 2*a*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x))","F",0
190,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-5/2), x)","F",0
191,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**(5/2),x)","\frac{\int \frac{1}{a^{2} c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + a^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 2 a b c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 2 a b d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + b^{2} c \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{2} d x \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c*sqrt(a + b*acosh(c + d*x)) + a**2*d*x*sqrt(a + b*acosh(c + d*x)) + 2*a*b*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 2*a*b*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + b**2*c*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**2*d*x*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2), x)/e","F",0
192,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*acosh(d*x+c))**(7/2),x)","e^{4} \left(\int \frac{c^{4}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(d**4*x**4/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(4*c*d**3*x**3/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(6*c**2*d**2*x**2/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(4*c**3*d*x/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x))","F",0
193,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*acosh(d*x+c))**(7/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(d**3*x**3/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x))","F",0
194,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*acosh(d*x+c))**(7/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(d**2*x**2/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(2*c*d*x/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x))","F",0
195,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*acosh(d*x+c))**(7/2),x)","e \left(\int \frac{c}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{acosh}{\left(c + d x \right)}} \operatorname{acosh}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x) + Integral(d*x/(a**3*sqrt(a + b*acosh(c + d*x)) + 3*a**2*b*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x) + 3*a*b**2*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**2 + b**3*sqrt(a + b*acosh(c + d*x))*acosh(c + d*x)**3), x))","F",0
196,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**(-7/2), x)","F",0
197,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*acosh(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*acosh(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*acosh(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*acosh(d*x+c)),x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*acosh(c + d*x)), x)","F",0
201,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*acosh(c + d*x)), x)","F",0
202,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**(1/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c + d x \right)}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))/sqrt(e*(c + d*x)), x)","F",0
203,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**(3/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))/(e*(c + d*x))**(3/2), x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**(5/2),x)","\int \frac{a + b \operatorname{acosh}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))/(e*(c + d*x))**(5/2), x)","F",0
205,-1,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*acosh(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*acosh(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*acosh(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*acosh(c + d*x))**2, x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))**2, x)","F",0
210,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**2/sqrt(e*(c + d*x)), x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**2/(e*(c + d*x))**(3/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**2/(e*(c + d*x))**(5/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**2/(d*e*x+c*e)**(7/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**2/(e*(c + d*x))**(7/2), x)","F",0
214,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*acosh(d*x+c))**3,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*acosh(c + d*x))**3, x)","F",0
215,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))**3, x)","F",0
216,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**3/sqrt(e*(c + d*x)), x)","F",0
217,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**3/(e*(c + d*x))**(3/2), x)","F",0
218,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**3/(e*(c + d*x))**(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**3/(d*e*x+c*e)**(7/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**3/(e*(c + d*x))**(7/2), x)","F",0
220,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*acosh(d*x+c))**4,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*acosh(c + d*x))**4, x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4*(d*e*x+c*e)**(1/2),x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))**4, x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**(1/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}}{\sqrt{e \left(c + d x\right)}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**4/sqrt(e*(c + d*x)), x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**4/(e*(c + d*x))**(3/2), x)","F",0
224,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**4/(e*(c + d*x))**(5/2), x)","F",0
225,0,0,0,0.000000," ","integrate((a+b*acosh(d*x+c))**4/(d*e*x+c*e)**(7/2),x)","\int \frac{\left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(c + d*x))**4/(e*(c + d*x))**(7/2), x)","F",0
226,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*acosh(d*x+c))**4,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*acosh(c + d*x))**4, x)","F",0
227,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*acosh(d*x+c))**3,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*acosh(c + d*x))**3, x)","F",0
228,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*acosh(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*acosh(c + d*x))**2, x)","F",0
229,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*acosh(d*x+c)),x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{acosh}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*acosh(c + d*x)), x)","F",0
230,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m/(a+b*acosh(d*x+c)),x)","\int \frac{\left(e \left(c + d x\right)\right)^{m}}{a + b \operatorname{acosh}{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*(c + d*x))**m/(a + b*acosh(c + d*x)), x)","F",0
231,0,0,0,0.000000," ","integrate(acosh(a*x**5)/x,x)","\int \frac{\operatorname{acosh}{\left(a x^{5} \right)}}{x}\, dx"," ",0,"Integral(acosh(a*x**5)/x, x)","F",0
232,0,0,0,0.000000," ","integrate(x**2*acosh(x**(1/2)),x)","\int x^{2} \operatorname{acosh}{\left(\sqrt{x} \right)}\, dx"," ",0,"Integral(x**2*acosh(sqrt(x)), x)","F",0
233,0,0,0,0.000000," ","integrate(x*acosh(x**(1/2)),x)","\int x \operatorname{acosh}{\left(\sqrt{x} \right)}\, dx"," ",0,"Integral(x*acosh(sqrt(x)), x)","F",0
234,1,29,0,0.257327," ","integrate(acosh(x**(1/2)),x)","- \frac{\sqrt{x} \sqrt{x - 1}}{2} + x \operatorname{acosh}{\left(\sqrt{x} \right)} - \frac{\operatorname{acosh}{\left(\sqrt{x} \right)}}{2}"," ",0,"-sqrt(x)*sqrt(x - 1)/2 + x*acosh(sqrt(x)) - acosh(sqrt(x))/2","A",0
235,0,0,0,0.000000," ","integrate(acosh(x**(1/2))/x,x)","\int \frac{\operatorname{acosh}{\left(\sqrt{x} \right)}}{x}\, dx"," ",0,"Integral(acosh(sqrt(x))/x, x)","F",0
236,0,0,0,0.000000," ","integrate(acosh(x**(1/2))/x**2,x)","\int \frac{\operatorname{acosh}{\left(\sqrt{x} \right)}}{x^{2}}\, dx"," ",0,"Integral(acosh(sqrt(x))/x**2, x)","F",0
237,0,0,0,0.000000," ","integrate(acosh(x**(1/2))/x**3,x)","\int \frac{\operatorname{acosh}{\left(\sqrt{x} \right)}}{x^{3}}\, dx"," ",0,"Integral(acosh(sqrt(x))/x**3, x)","F",0
238,0,0,0,0.000000," ","integrate(acosh(1/x),x)","\int \operatorname{acosh}{\left(\frac{1}{x} \right)}\, dx"," ",0,"Integral(acosh(1/x), x)","F",0
239,0,0,0,0.000000," ","integrate(acosh(a*x**n)/x,x)","\int \frac{\operatorname{acosh}{\left(a x^{n} \right)}}{x}\, dx"," ",0,"Integral(acosh(a*x**n)/x, x)","F",0
240,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**4,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{4}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**4, x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**3,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**3, x)","F",0
242,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**2,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**2, x)","F",0
243,0,0,0,0.000000," ","integrate(a+b*acosh(d*x**2+1),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)\, dx"," ",0,"Integral(a + b*acosh(d*x**2 + 1), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1)),x)","\int \frac{1}{a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}}\, dx"," ",0,"Integral(1/(a + b*acosh(d*x**2 + 1)), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**2,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(-2), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**3,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(-3), x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**4,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{4}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**4, x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**3,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**3, x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**2,x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**2, x)","F",0
250,0,0,0,0.000000," ","integrate(a+b*acosh(d*x**2-1),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)\, dx"," ",0,"Integral(a + b*acosh(d*x**2 - 1), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1)),x)","\int \frac{1}{a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}}\, dx"," ",0,"Integral(1/(a + b*acosh(d*x**2 - 1)), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**2,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(-2), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**3,x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(-3), x)","F",0
254,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**(5/2),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(5/2), x)","F",0
255,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**(3/2),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(3/2), x)","F",0
256,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2+1))**(1/2),x)","\int \sqrt{a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}}\, dx"," ",0,"Integral(sqrt(a + b*acosh(d*x**2 + 1)), x)","F",0
257,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*acosh(d*x**2 + 1)), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(-3/2), x)","F",0
259,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(-5/2), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2+1))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} + 1 \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 + 1))**(-7/2), x)","F",0
261,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**(5/2),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(5/2), x)","F",0
262,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**(3/2),x)","\int \left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*acosh(d*x**2-1))**(1/2),x)","\int \sqrt{a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}}\, dx"," ",0,"Integral(sqrt(a + b*acosh(d*x**2 - 1)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*acosh(d*x**2 - 1)), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(-3/2), x)","F",0
266,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(-5/2), x)","F",0
267,0,0,0,0.000000," ","integrate(1/(a+b*acosh(d*x**2-1))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{acosh}{\left(d x^{2} - 1 \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*acosh(d*x**2 - 1))**(-7/2), x)","F",0
268,-1,0,0,0.000000," ","integrate((a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**n/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,0,0,0,0.000000," ","integrate((a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**3/(-c**2*x**2+1),x)","- \int \frac{a^{3}}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{3} \operatorname{acosh}^{3}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{3 a b^{2} \operatorname{acosh}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{3 a^{2} b \operatorname{acosh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a**3/(c**2*x**2 - 1), x) - Integral(b**3*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))**3/(c**2*x**2 - 1), x) - Integral(3*a*b**2*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))**2/(c**2*x**2 - 1), x) - Integral(3*a**2*b*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
270,0,0,0,0.000000," ","integrate((a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2/(-c**2*x**2+1),x)","- \int \frac{a^{2}}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{2} \operatorname{acosh}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{2 a b \operatorname{acosh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a**2/(c**2*x**2 - 1), x) - Integral(b**2*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))**2/(c**2*x**2 - 1), x) - Integral(2*a*b*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
271,0,0,0,0.000000," ","integrate((a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))/(-c**2*x**2+1),x)","- \int \frac{a}{c^{2} x^{2} - 1}\, dx - \int \frac{b \operatorname{acosh}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a/(c**2*x**2 - 1), x) - Integral(b*acosh(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c**2*x**2 - 1), x)","F",0
272,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*acosh((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,0,0,0,0.000000," ","integrate(acosh(c*exp(b*x+a)),x)","\int \operatorname{acosh}{\left(c e^{a + b x} \right)}\, dx"," ",0,"Integral(acosh(c*exp(a + b*x)), x)","F",0
275,0,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))*x**3,x)","\int x^{3} \left(a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}\right)\, dx"," ",0,"Integral(x**3*(a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1)), x)","F",0
276,0,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))*x**2,x)","\int x^{2} \left(a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}\right)\, dx"," ",0,"Integral(x**2*(a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1)), x)","F",0
277,0,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))*x,x)","\int x \left(a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}\right)\, dx"," ",0,"Integral(x*(a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1)), x)","F",0
278,0,0,0,0.000000," ","integrate(b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2),x)","\int \left(a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}\right)\, dx"," ",0,"Integral(a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1), x)","F",0
279,0,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))/x,x)","\int \frac{a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}}{x}\, dx"," ",0,"Integral((a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1))/x, x)","F",0
280,0,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))/x**2,x)","\int \frac{a + b x + \sqrt{a + b x - 1} \sqrt{a + b x + 1}}{x^{2}}\, dx"," ",0,"Integral((a + b*x + sqrt(a + b*x - 1)*sqrt(a + b*x + 1))/x**2, x)","F",0
281,-1,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)**(1/2)*(b*x+a+1)**(1/2))/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2)*x**3,x)","\int x^{3} e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**3*exp(acosh(a + b*x)**2), x)","F",0
285,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2)*x**2,x)","\int x^{2} e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2*exp(acosh(a + b*x)**2), x)","F",0
286,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2)*x,x)","\int x e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*exp(acosh(a + b*x)**2), x)","F",0
287,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2),x)","\int e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(exp(acosh(a + b*x)**2), x)","F",0
288,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2)/x,x)","\int \frac{e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(exp(acosh(a + b*x)**2)/x, x)","F",0
289,0,0,0,0.000000," ","integrate(exp(acosh(b*x+a)**2)/x**2,x)","\int \frac{e^{\operatorname{acosh}^{2}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(acosh(a + b*x)**2)/x**2, x)","F",0
290,0,0,0,0.000000," ","integrate(acosh(b*x+a)/(a*d/b+d*x),x)","\frac{b \int \frac{\operatorname{acosh}{\left(a + b x \right)}}{a + b x}\, dx}{d}"," ",0,"b*Integral(acosh(a + b*x)/(a + b*x), x)/d","F",0
291,0,0,0,0.000000," ","integrate(x/acosh(x)/(-1+x)**(1/2)/(1+x)**(1/2),x)","\int \frac{x}{\sqrt{x - 1} \sqrt{x + 1} \operatorname{acosh}{\left(x \right)}}\, dx"," ",0,"Integral(x/(sqrt(x - 1)*sqrt(x + 1)*acosh(x)), x)","F",0
292,1,61,0,0.788300," ","integrate(x**3*acosh(b*x**4+a),x)","\begin{cases} \frac{a \operatorname{acosh}{\left(a + b x^{4} \right)}}{4 b} + \frac{x^{4} \operatorname{acosh}{\left(a + b x^{4} \right)}}{4} - \frac{\sqrt{a^{2} + 2 a b x^{4} + b^{2} x^{8} - 1}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{acosh}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*acosh(a + b*x**4)/(4*b) + x**4*acosh(a + b*x**4)/4 - sqrt(a**2 + 2*a*b*x**4 + b**2*x**8 - 1)/(4*b), Ne(b, 0)), (x**4*acosh(a)/4, True))","A",0
293,1,76,0,58.148189," ","integrate(x**(-1+n)*acosh(a+b*x**n),x)","\begin{cases} \log{\left(x \right)} \operatorname{acosh}{\left(a \right)} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{n} \operatorname{acosh}{\left(a \right)}}{n} & \text{for}\: b = 0 \\\log{\left(x \right)} \operatorname{acosh}{\left(a + b \right)} & \text{for}\: n = 0 \\\frac{a \operatorname{acosh}{\left(a + b x^{n} \right)}}{b n} + \frac{x^{n} \operatorname{acosh}{\left(a + b x^{n} \right)}}{n} - \frac{\sqrt{a^{2} + 2 a b x^{n} + b^{2} x^{2 n} - 1}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)*acosh(a), Eq(b, 0) & Eq(n, 0)), (x**n*acosh(a)/n, Eq(b, 0)), (log(x)*acosh(a + b), Eq(n, 0)), (a*acosh(a + b*x**n)/(b*n) + x**n*acosh(a + b*x**n)/n - sqrt(a**2 + 2*a*b*x**n + b**2*x**(2*n) - 1)/(b*n), True))","A",0
294,0,0,0,0.000000," ","integrate(acosh(c/(b*x+a)),x)","\int \operatorname{acosh}{\left(\frac{c}{a + b x} \right)}\, dx"," ",0,"Integral(acosh(c/(a + b*x)), x)","F",0
295,0,0,0,0.000000," ","integrate(acosh((b*x**2+1)**(1/2))**n/(b*x**2+1)**(1/2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: b = 0 \wedge n = -1 \\0^{n} x & \text{for}\: b = 0 \\\int \frac{1}{\sqrt{b x^{2} + 1} \operatorname{acosh}{\left(\sqrt{b x^{2} + 1} \right)}}\, dx & \text{for}\: n = -1 \\\frac{\sqrt{b} \sqrt{x^{2}} \operatorname{acosh}{\left(\sqrt{b x^{2} + 1} \right)} \operatorname{acosh}^{n}{\left(\sqrt{b x^{2} + 1} \right)}}{b n x + b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(b, 0) & Eq(n, -1)), (0**n*x, Eq(b, 0)), (Integral(1/(sqrt(b*x**2 + 1)*acosh(sqrt(b*x**2 + 1))), x), Eq(n, -1)), (sqrt(b)*sqrt(x**2)*acosh(sqrt(b*x**2 + 1))*acosh(sqrt(b*x**2 + 1))**n/(b*n*x + b*x), True))","F",0
296,0,0,0,0.000000," ","integrate(1/acosh((b*x**2+1)**(1/2))/(b*x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} + 1} \operatorname{acosh}{\left(\sqrt{b x^{2} + 1} \right)}}\, dx"," ",0,"Integral(1/(sqrt(b*x**2 + 1)*acosh(sqrt(b*x**2 + 1))), x)","F",0
