3.5.95 \(\int \frac {\coth ^5(e+f x)}{(a+b \sinh ^2(e+f x))^{3/2}} \, dx\) [495]

Optimal. Leaf size=167 \[ -\frac {\left (8 a^2-24 a b+15 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \sinh ^2(e+f x)}}{\sqrt {a}}\right )}{8 a^{7/2} f}+\frac {8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}} \]

[Out]

-1/8*(8*a^2-24*a*b+15*b^2)*arctanh((a+b*sinh(f*x+e)^2)^(1/2)/a^(1/2))/a^(7/2)/f+1/8*(8*a^2-24*a*b+15*b^2)/a^3/
f/(a+b*sinh(f*x+e)^2)^(1/2)-1/8*(8*a-5*b)*csch(f*x+e)^2/a^2/f/(a+b*sinh(f*x+e)^2)^(1/2)-1/4*csch(f*x+e)^4/a/f/
(a+b*sinh(f*x+e)^2)^(1/2)

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Rubi [A]
time = 0.14, antiderivative size = 167, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 6, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.240, Rules used = {3273, 91, 79, 53, 65, 214} \begin {gather*} -\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\left (8 a^2-24 a b+15 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \sinh ^2(e+f x)}}{\sqrt {a}}\right )}{8 a^{7/2} f}+\frac {8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Coth[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(3/2),x]

[Out]

-1/8*((8*a^2 - 24*a*b + 15*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(a^(7/2)*f) + (8*a^2 - 24*a*b +
15*b^2)/(8*a^3*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((8*a - 5*b)*Csch[e + f*x]^2)/(8*a^2*f*Sqrt[a + b*Sinh[e + f*x
]^2]) - Csch[e + f*x]^4/(4*a*f*Sqrt[a + b*Sinh[e + f*x]^2])

Rule 53

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[(a + b*x)^(m + 1)*((c + d*x)^(n + 1
)/((b*c - a*d)*(m + 1))), x] - Dist[d*((m + n + 2)/((b*c - a*d)*(m + 1))), Int[(a + b*x)^(m + 1)*(c + d*x)^n,
x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && LtQ[m, -1] &&  !(LtQ[n, -1] && (EqQ[a, 0] || (NeQ[
c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && IntLinearQ[a, b, c, d, m, n, x]

Rule 65

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - a*(d/b) + d*(x^p/b))^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 79

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(-(b*e - a*f
))*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(f*(p + 1)*(c*f - d*e))), x] - Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1
) + c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)), Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e,
f, n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || IntegerQ[p] ||  !(IntegerQ[n] ||  !(EqQ[e, 0] ||  !(EqQ[c, 0] || L
tQ[p, n]))))

Rule 91

Int[((a_.) + (b_.)*(x_))^2*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*c - a*d
)^2*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(d^2*(d*e - c*f)*(n + 1))), x] - Dist[1/(d^2*(d*e - c*f)*(n + 1)), In
t[(c + d*x)^(n + 1)*(e + f*x)^p*Simp[a^2*d^2*f*(n + p + 2) + b^2*c*(d*e*(n + 1) + c*f*(p + 1)) - 2*a*b*d*(d*e*
(n + 1) + c*f*(p + 1)) - b^2*d*(d*e - c*f)*(n + 1)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && (LtQ
[n, -1] || (EqQ[n + p + 3, 0] && NeQ[n, -1] && (SumSimplerQ[n, 1] ||  !SumSimplerQ[p, 1])))

Rule 214

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-a/b, 2]/a)*ArcTanh[x/Rt[-a/b, 2]], x] /; FreeQ[{a, b},
x] && NegQ[a/b]

Rule 3273

Int[((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]^2)^(p_.)*tan[(e_.) + (f_.)*(x_)]^(m_.), x_Symbol] :> With[{ff = Free
Factors[Sin[e + f*x]^2, x]}, Dist[ff^((m + 1)/2)/(2*f), Subst[Int[x^((m - 1)/2)*((a + b*ff*x)^p/(1 - ff*x)^((m
+ 1)/2)), x], x, Sin[e + f*x]^2/ff], x]] /; FreeQ[{a, b, e, f, p}, x] && IntegerQ[(m - 1)/2]

Rubi steps

\begin {align*} \int \frac {\coth ^5(e+f x)}{\left (a+b \sinh ^2(e+f x)\right )^{3/2}} \, dx &=\frac {\text {Subst}\left (\int \frac {(1+x)^2}{x^3 (a+b x)^{3/2}} \, dx,x,\sinh ^2(e+f x)\right )}{2 f}\\ &=-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}}+\frac {\text {Subst}\left (\int \frac {\frac {1}{2} (8 a-5 b)+2 a x}{x^2 (a+b x)^{3/2}} \, dx,x,\sinh ^2(e+f x)\right )}{4 a f}\\ &=-\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}}+\frac {\left (8 a^2-24 a b+15 b^2\right ) \text {Subst}\left (\int \frac {1}{x (a+b x)^{3/2}} \, dx,x,\sinh ^2(e+f x)\right )}{16 a^2 f}\\ &=\frac {8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}}+\frac {\left (8 a^2-24 a b+15 b^2\right ) \text {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,\sinh ^2(e+f x)\right )}{16 a^3 f}\\ &=\frac {8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}}+\frac {\left (8 a^2-24 a b+15 b^2\right ) \text {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \sinh ^2(e+f x)}\right )}{8 a^3 b f}\\ &=-\frac {\left (8 a^2-24 a b+15 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {a+b \sinh ^2(e+f x)}}{\sqrt {a}}\right )}{8 a^{7/2} f}+\frac {8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {(8 a-5 b) \text {csch}^2(e+f x)}{8 a^2 f \sqrt {a+b \sinh ^2(e+f x)}}-\frac {\text {csch}^4(e+f x)}{4 a f \sqrt {a+b \sinh ^2(e+f x)}}\\ \end {align*}

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Mathematica [C] Result contains higher order function than in optimal. Order 5 vs. order 3 in optimal.
time = 0.23, size = 94, normalized size = 0.56 \begin {gather*} \frac {a \text {csch}^2(e+f x) \left (-8 a+5 b-2 a \text {csch}^2(e+f x)\right )+\left (8 a^2-24 a b+15 b^2\right ) \, _2F_1\left (-\frac {1}{2},1;\frac {1}{2};1+\frac {b \sinh ^2(e+f x)}{a}\right )}{8 a^3 f \sqrt {a+b \sinh ^2(e+f x)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Coth[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(3/2),x]

[Out]

(a*Csch[e + f*x]^2*(-8*a + 5*b - 2*a*Csch[e + f*x]^2) + (8*a^2 - 24*a*b + 15*b^2)*Hypergeometric2F1[-1/2, 1, 1
/2, 1 + (b*Sinh[e + f*x]^2)/a])/(8*a^3*f*Sqrt[a + b*Sinh[e + f*x]^2])

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 8.83, size = 43, normalized size = 0.26

method	result	size
default	\(\frac {\mathit {`\,int/indef0`\,}\left (\frac {\cosh ^{4}\left (f x +e \right )}{\sinh \left (f x +e \right )^{5} \left (a +b \left (\sinh ^{2}\left (f x +e \right )\right )\right )^{\frac {3}{2}}}, \sinh \left (f x +e \right )\right )}{f}\)	\(43\)
risch	\(\text {Expression too large to display}\)	\(2583800\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x,method=_RETURNVERBOSE)

[Out]

`int/indef0`(cosh(f*x+e)^4/sinh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),sinh(f*x+e))/f

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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm="maxima")

[Out]

integrate(coth(f*x + e)^5/(b*sinh(f*x + e)^2 + a)^(3/2), x)

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 3680 vs. \(2 (147) = 294\).
time = 0.72, size = 7562, normalized size = 45.28 \begin {gather*} \text {too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm="fricas")

[Out]

[1/16*(((8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^12 + 12*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)*sinh(f
*x + e)^11 + (8*a^2*b - 24*a*b^2 + 15*b^3)*sinh(f*x + e)^12 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(
f*x + e)^10 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3 + 33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^2)*si
nh(f*x + e)^10 + 20*(11*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^
3)*cosh(f*x + e))*sinh(f*x + e)^9 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^8 + (495*(8*a^2*
b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 90*(16*a^3 - 72*a^2*b + 1
02*a*b^2 - 45*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^5 + 30
*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^3 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f
*x + e))*sinh(f*x + e)^7 + 4*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^6 + 4*(231*(8*a^2*b - 24*
a*b^2 + 15*b^3)*cosh(f*x + e)^6 + 105*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^4 + 48*a^3 - 184*
a^2*b + 210*a*b^2 - 75*b^3 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 +
8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^7 + 63*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e
)^5 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + 3*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b
^3)*cosh(f*x + e))*sinh(f*x + e)^5 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 + (495*(8*a^2
*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^8 + 420*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^6 - 70*(1
28*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 60*(48
*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(8*a^2*b - 24*a*b^2 + 15*b^3)*
cosh(f*x + e)^9 + 60*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^7 - 14*(128*a^3 - 504*a^2*b + 600*
a*b^2 - 225*b^3)*cosh(f*x + e)^5 + 20*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^3 - (128*a^3 - 5
04*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*a^2*b - 24*a*b^2 + 15*b^3 + 2*(16*a^3 - 72*
a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^2 + 2*(33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^10 + 45*(16*a^
3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^8 - 14*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x +
e)^6 + 30*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + 16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3
- 3*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(8*a^2*b - 24*a*b^2 +
15*b^3)*cosh(f*x + e)^11 + 5*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^9 - 2*(128*a^3 - 504*a^2*b
+ 600*a*b^2 - 225*b^3)*cosh(f*x + e)^7 + 6*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^5 - (128*a
^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)
)*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4
*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f
*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*
(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x
+ e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*co
sh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((8*a^3 - 24*a^2*b + 15*a*
b^2)*cosh(f*x + e)^9 + 9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^3 - 24*a^2*b + 15*
a*b^2)*sinh(f*x + e)^9 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2 -
9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(3*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*
x + e)^3 - (16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(40*a^3 - 92*a^2*b + 45*a*b^2)*co
sh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 + 40*a^3 - 92*a^2*b + 45*a*b^2 - 42*(16*a^
3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^
5 - 70*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e))*sinh(f
*x + e)^4 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x +
e)^6 - 35*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 - 16*a^3 + 29*a^2*b - 15*a*b^2 + 5*(40*a^3 - 92*a^2*b
+ 45*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 21*(16*a^
3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^3 - 3*(16*a^3 - 29*a
^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e) + (9*(8*a^3 - 24
*a^2*b + 15*a*b^2)*cosh(f*x + e)^8 - 28*(16*a^3...

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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\coth ^{5}{\left (e + f x \right )}}{\left (a + b \sinh ^{2}{\left (e + f x \right )}\right )^{\frac {3}{2}}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(coth(f*x+e)**5/(a+b*sinh(f*x+e)**2)**(3/2),x)

[Out]

Integral(coth(e + f*x)**5/(a + b*sinh(e + f*x)**2)**(3/2), x)

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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 2.63Error: Bad Argument Type

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Mupad [F(-1)]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(coth(e + f*x)^5/(a + b*sinh(e + f*x)^2)^(3/2),x)

[Out]

\text{Hanged}

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