3.1.55 \(\int \text {csch}^3(c+d x) (a+b \tanh ^3(c+d x)) \, dx\) [55]

Optimal. Leaf size=71 \[ \frac {b \text {ArcTan}(\sinh (c+d x))}{2 d}+\frac {a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac {a \coth (c+d x) \text {csch}(c+d x)}{2 d}+\frac {b \text {sech}(c+d x) \tanh (c+d x)}{2 d} \]

[Out]

1/2*b*arctan(sinh(d*x+c))/d+1/2*a*arctanh(cosh(d*x+c))/d-1/2*a*coth(d*x+c)*csch(d*x+c)/d+1/2*b*sech(d*x+c)*tan
h(d*x+c)/d

________________________________________________________________________________________

Rubi [A]
time = 0.07, antiderivative size = 71, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {3747, 3853, 3855} \begin {gather*} \frac {a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac {a \coth (c+d x) \text {csch}(c+d x)}{2 d}+\frac {b \text {ArcTan}(\sinh (c+d x))}{2 d}+\frac {b \tanh (c+d x) \text {sech}(c+d x)}{2 d} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^3),x]

[Out]

(b*ArcTan[Sinh[c + d*x]])/(2*d) + (a*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d) + (
b*Sech[c + d*x]*Tanh[c + d*x])/(2*d)

Rule 3747

Int[((d_.)*sin[(e_.) + (f_.)*(x_)])^(m_.)*((a_) + (b_.)*((c_.)*tan[(e_.) + (f_.)*(x_)])^(n_))^(p_.), x_Symbol]
:> Int[ExpandTrig[(d*sin[e + f*x])^m*(a + b*(c*tan[e + f*x])^n)^p, x], x] /; FreeQ[{a, b, c, d, e, f, m, n},
x] && IGtQ[p, 0]

Rule 3853

Int[(csc[(c_.) + (d_.)*(x_)]*(b_.))^(n_), x_Symbol] :> Simp[(-b)*Cos[c + d*x]*((b*Csc[c + d*x])^(n - 1)/(d*(n
- 1))), x] + Dist[b^2*((n - 2)/(n - 1)), Int[(b*Csc[c + d*x])^(n - 2), x], x] /; FreeQ[{b, c, d}, x] && GtQ[n,
1] && IntegerQ[2*n]

Rule 3855

Int[csc[(c_.) + (d_.)*(x_)], x_Symbol] :> Simp[-ArcTanh[Cos[c + d*x]]/d, x] /; FreeQ[{c, d}, x]

Rubi steps

\begin {align*} \int \text {csch}^3(c+d x) \left (a+b \tanh ^3(c+d x)\right ) \, dx &=-\left (i \int \left (i a \text {csch}^3(c+d x)+i b \text {sech}^3(c+d x)\right ) \, dx\right )\\ &=a \int \text {csch}^3(c+d x) \, dx+b \int \text {sech}^3(c+d x) \, dx\\ &=-\frac {a \coth (c+d x) \text {csch}(c+d x)}{2 d}+\frac {b \text {sech}(c+d x) \tanh (c+d x)}{2 d}-\frac {1}{2} a \int \text {csch}(c+d x) \, dx+\frac {1}{2} b \int \text {sech}(c+d x) \, dx\\ &=\frac {b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac {a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac {a \coth (c+d x) \text {csch}(c+d x)}{2 d}+\frac {b \text {sech}(c+d x) \tanh (c+d x)}{2 d}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.02, size = 95, normalized size = 1.34 \begin {gather*} \frac {b \text {ArcTan}(\sinh (c+d x))}{2 d}-\frac {a \text {csch}^2\left (\frac {1}{2} (c+d x)\right )}{8 d}-\frac {a \log \left (\tanh \left (\frac {1}{2} (c+d x)\right )\right )}{2 d}-\frac {a \text {sech}^2\left (\frac {1}{2} (c+d x)\right )}{8 d}+\frac {b \text {sech}(c+d x) \tanh (c+d x)}{2 d} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^3),x]

[Out]

(b*ArcTan[Sinh[c + d*x]])/(2*d) - (a*Csch[(c + d*x)/2]^2)/(8*d) - (a*Log[Tanh[(c + d*x)/2]])/(2*d) - (a*Sech[(
c + d*x)/2]^2)/(8*d) + (b*Sech[c + d*x]*Tanh[c + d*x])/(2*d)

________________________________________________________________________________________

Maple [C] Result contains complex when optimal does not.
time = 3.20, size = 177, normalized size = 2.49

method	result	size
risch	\(-\frac {{\mathrm e}^{d x +c} \left (a \,{\mathrm e}^{6 d x +6 c}-b \,{\mathrm e}^{6 d x +6 c}+3 a \,{\mathrm e}^{4 d x +4 c}+3 b \,{\mathrm e}^{4 d x +4 c}+3 a \,{\mathrm e}^{2 d x +2 c}-3 b \,{\mathrm e}^{2 d x +2 c}+a +b \right )}{d \left ({\mathrm e}^{2 d x +2 c}-1\right )^{2} \left (1+{\mathrm e}^{2 d x +2 c}\right )^{2}}+\frac {a \ln \left ({\mathrm e}^{d x +c}+1\right )}{2 d}-\frac {a \ln \left ({\mathrm e}^{d x +c}-1\right )}{2 d}+\frac {i b \ln \left ({\mathrm e}^{d x +c}+i\right )}{2 d}-\frac {i b \ln \left ({\mathrm e}^{d x +c}-i\right )}{2 d}\)	\(177\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x,method=_RETURNVERBOSE)

[Out]

-exp(d*x+c)*(a*exp(6*d*x+6*c)-b*exp(6*d*x+6*c)+3*a*exp(4*d*x+4*c)+3*b*exp(4*d*x+4*c)+3*a*exp(2*d*x+2*c)-3*b*ex
p(2*d*x+2*c)+a+b)/d/(exp(2*d*x+2*c)-1)^2/(1+exp(2*d*x+2*c))^2+1/2*a/d*ln(exp(d*x+c)+1)-1/2*a/d*ln(exp(d*x+c)-1
)+1/2*I*b/d*ln(exp(d*x+c)+I)-1/2*I*b/d*ln(exp(d*x+c)-I)

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 156 vs. \(2 (63) = 126\).
time = 0.49, size = 156, normalized size = 2.20 \begin {gather*} -b {\left (\frac {\arctan \left (e^{\left (-d x - c\right )}\right )}{d} - \frac {e^{\left (-d x - c\right )} - e^{\left (-3 \, d x - 3 \, c\right )}}{d {\left (2 \, e^{\left (-2 \, d x - 2 \, c\right )} + e^{\left (-4 \, d x - 4 \, c\right )} + 1\right )}}\right )} + \frac {1}{2} \, a {\left (\frac {\log \left (e^{\left (-d x - c\right )} + 1\right )}{d} - \frac {\log \left (e^{\left (-d x - c\right )} - 1\right )}{d} + \frac {2 \, {\left (e^{\left (-d x - c\right )} + e^{\left (-3 \, d x - 3 \, c\right )}\right )}}{d {\left (2 \, e^{\left (-2 \, d x - 2 \, c\right )} - e^{\left (-4 \, d x - 4 \, c\right )} - 1\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm="maxima")

[Out]

-b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))
) + 1/2*a*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2
*d*x - 2*c) - e^(-4*d*x - 4*c) - 1)))

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1188 vs. \(2 (63) = 126\).
time = 0.38, size = 1188, normalized size = 16.73 \begin {gather*} -\frac {2 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{7} + 14 \, {\left (a - b\right )} \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{6} + 2 \, {\left (a - b\right )} \sinh \left (d x + c\right )^{7} + 6 \, {\left (a + b\right )} \cosh \left (d x + c\right )^{5} + 6 \, {\left (7 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{2} + a + b\right )} \sinh \left (d x + c\right )^{5} + 10 \, {\left (7 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{3} + 3 \, {\left (a + b\right )} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{4} + 6 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{3} + 2 \, {\left (35 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{4} + 30 \, {\left (a + b\right )} \cosh \left (d x + c\right )^{2} + 3 \, a - 3 \, b\right )} \sinh \left (d x + c\right )^{3} + 6 \, {\left (7 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{5} + 10 \, {\left (a + b\right )} \cosh \left (d x + c\right )^{3} + 3 \, {\left (a - b\right )} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{2} - 2 \, {\left (b \cosh \left (d x + c\right )^{8} + 56 \, b \cosh \left (d x + c\right )^{3} \sinh \left (d x + c\right )^{5} + 28 \, b \cosh \left (d x + c\right )^{2} \sinh \left (d x + c\right )^{6} + 8 \, b \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{7} + b \sinh \left (d x + c\right )^{8} - 2 \, b \cosh \left (d x + c\right )^{4} + 2 \, {\left (35 \, b \cosh \left (d x + c\right )^{4} - b\right )} \sinh \left (d x + c\right )^{4} + 8 \, {\left (7 \, b \cosh \left (d x + c\right )^{5} - b \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{3} + 4 \, {\left (7 \, b \cosh \left (d x + c\right )^{6} - 3 \, b \cosh \left (d x + c\right )^{2}\right )} \sinh \left (d x + c\right )^{2} + 8 \, {\left (b \cosh \left (d x + c\right )^{7} - b \cosh \left (d x + c\right )^{3}\right )} \sinh \left (d x + c\right ) + b\right )} \arctan \left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right )\right ) + 2 \, {\left (a + b\right )} \cosh \left (d x + c\right ) - {\left (a \cosh \left (d x + c\right )^{8} + 56 \, a \cosh \left (d x + c\right )^{3} \sinh \left (d x + c\right )^{5} + 28 \, a \cosh \left (d x + c\right )^{2} \sinh \left (d x + c\right )^{6} + 8 \, a \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{7} + a \sinh \left (d x + c\right )^{8} - 2 \, a \cosh \left (d x + c\right )^{4} + 2 \, {\left (35 \, a \cosh \left (d x + c\right )^{4} - a\right )} \sinh \left (d x + c\right )^{4} + 8 \, {\left (7 \, a \cosh \left (d x + c\right )^{5} - a \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{3} + 4 \, {\left (7 \, a \cosh \left (d x + c\right )^{6} - 3 \, a \cosh \left (d x + c\right )^{2}\right )} \sinh \left (d x + c\right )^{2} + 8 \, {\left (a \cosh \left (d x + c\right )^{7} - a \cosh \left (d x + c\right )^{3}\right )} \sinh \left (d x + c\right ) + a\right )} \log \left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right ) + 1\right ) + {\left (a \cosh \left (d x + c\right )^{8} + 56 \, a \cosh \left (d x + c\right )^{3} \sinh \left (d x + c\right )^{5} + 28 \, a \cosh \left (d x + c\right )^{2} \sinh \left (d x + c\right )^{6} + 8 \, a \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{7} + a \sinh \left (d x + c\right )^{8} - 2 \, a \cosh \left (d x + c\right )^{4} + 2 \, {\left (35 \, a \cosh \left (d x + c\right )^{4} - a\right )} \sinh \left (d x + c\right )^{4} + 8 \, {\left (7 \, a \cosh \left (d x + c\right )^{5} - a \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{3} + 4 \, {\left (7 \, a \cosh \left (d x + c\right )^{6} - 3 \, a \cosh \left (d x + c\right )^{2}\right )} \sinh \left (d x + c\right )^{2} + 8 \, {\left (a \cosh \left (d x + c\right )^{7} - a \cosh \left (d x + c\right )^{3}\right )} \sinh \left (d x + c\right ) + a\right )} \log \left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right ) - 1\right ) + 2 \, {\left (7 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{6} + 15 \, {\left (a + b\right )} \cosh \left (d x + c\right )^{4} + 9 \, {\left (a - b\right )} \cosh \left (d x + c\right )^{2} + a + b\right )} \sinh \left (d x + c\right )}{2 \, {\left (d \cosh \left (d x + c\right )^{8} + 56 \, d \cosh \left (d x + c\right )^{3} \sinh \left (d x + c\right )^{5} + 28 \, d \cosh \left (d x + c\right )^{2} \sinh \left (d x + c\right )^{6} + 8 \, d \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{7} + d \sinh \left (d x + c\right )^{8} - 2 \, d \cosh \left (d x + c\right )^{4} + 2 \, {\left (35 \, d \cosh \left (d x + c\right )^{4} - d\right )} \sinh \left (d x + c\right )^{4} + 8 \, {\left (7 \, d \cosh \left (d x + c\right )^{5} - d \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{3} + 4 \, {\left (7 \, d \cosh \left (d x + c\right )^{6} - 3 \, d \cosh \left (d x + c\right )^{2}\right )} \sinh \left (d x + c\right )^{2} + 8 \, {\left (d \cosh \left (d x + c\right )^{7} - d \cosh \left (d x + c\right )^{3}\right )} \sinh \left (d x + c\right ) + d\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm="fricas")

[Out]

-1/2*(2*(a - b)*cosh(d*x + c)^7 + 14*(a - b)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a - b)*sinh(d*x + c)^7 + 6*(a
+ b)*cosh(d*x + c)^5 + 6*(7*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^5 + 10*(7*(a - b)*cosh(d*x + c)^3 +
3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^3 + 2*(35*(a - b)*cosh(d*x + c)^4 + 30*(a
+ b)*cosh(d*x + c)^2 + 3*a - 3*b)*sinh(d*x + c)^3 + 6*(7*(a - b)*cosh(d*x + c)^5 + 10*(a + b)*cosh(d*x + c)^3
+ 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b*cosh(d*x + c)^8 + 56*b*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*
b*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 2*b*cosh(d*x + c)^
4 + 2*(35*b*cosh(d*x + c)^4 - b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - b*cosh(d*x + c))*sinh(d*x + c)^3 +
4*(7*b*cosh(d*x + c)^6 - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - b*cosh(d*x + c)^3)*sin
h(d*x + c) + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(a + b)*cosh(d*x + c) - (a*cosh(d*x + c)^8 + 56*a*co
sh(d*x + c)^3*sinh(d*x + c)^5 + 28*a*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a*cosh(d*x + c)*sinh(d*x + c)^7 + a*s
inh(d*x + c)^8 - 2*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 - a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*x + c)^5 -
a*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a*cosh(d*x + c)^6 - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a*cosh(
d*x + c)^7 - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a*cosh(d*x + c)^8
+ 56*a*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*a*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a*cosh(d*x + c)*sinh(d*x +
c)^7 + a*sinh(d*x + c)^8 - 2*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 - a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*
x + c)^5 - a*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a*cosh(d*x + c)^6 - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 +
8*(a*cosh(d*x + c)^7 - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(a
- b)*cosh(d*x + c)^6 + 15*(a + b)*cosh(d*x + c)^4 + 9*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c))/(d*cosh(
d*x + c)^8 + 56*d*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*d*cosh(d*x + c)*s
inh(d*x + c)^7 + d*sinh(d*x + c)^8 - 2*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 - d)*sinh(d*x + c)^4 + 8*(7
*d*cosh(d*x + c)^5 - d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*d*cosh(d*x + c)^6 - 3*d*cosh(d*x + c)^2)*sinh(d*x
+ c)^2 + 8*(d*cosh(d*x + c)^7 - d*cosh(d*x + c)^3)*sinh(d*x + c) + d)

________________________________________________________________________________________

Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b \tanh ^{3}{\left (c + d x \right )}\right ) \operatorname {csch}^{3}{\left (c + d x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)**3*(a+b*tanh(d*x+c)**3),x)

[Out]

Integral((a + b*tanh(c + d*x)**3)*csch(c + d*x)**3, x)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (63) = 126\).
time = 0.45, size = 143, normalized size = 2.01 \begin {gather*} \frac {2 \, b \arctan \left (e^{\left (d x + c\right )}\right ) + a \log \left (e^{\left (d x + c\right )} + 1\right ) - a \log \left ({\left | e^{\left (d x + c\right )} - 1 \right |}\right ) - \frac {2 \, {\left (a e^{\left (7 \, d x + 7 \, c\right )} - b e^{\left (7 \, d x + 7 \, c\right )} + 3 \, a e^{\left (5 \, d x + 5 \, c\right )} + 3 \, b e^{\left (5 \, d x + 5 \, c\right )} + 3 \, a e^{\left (3 \, d x + 3 \, c\right )} - 3 \, b e^{\left (3 \, d x + 3 \, c\right )} + a e^{\left (d x + c\right )} + b e^{\left (d x + c\right )}\right )}}{{\left (e^{\left (4 \, d x + 4 \, c\right )} - 1\right )}^{2}}}{2 \, d} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm="giac")

[Out]

1/2*(2*b*arctan(e^(d*x + c)) + a*log(e^(d*x + c) + 1) - a*log(abs(e^(d*x + c) - 1)) - 2*(a*e^(7*d*x + 7*c) - b
*e^(7*d*x + 7*c) + 3*a*e^(5*d*x + 5*c) + 3*b*e^(5*d*x + 5*c) + 3*a*e^(3*d*x + 3*c) - 3*b*e^(3*d*x + 3*c) + a*e
^(d*x + c) + b*e^(d*x + c))/(e^(4*d*x + 4*c) - 1)^2)/d

________________________________________________________________________________________

Mupad [B]
time = 2.48, size = 173, normalized size = 2.44 \begin {gather*} \frac {a\,\ln \left ({\mathrm {e}}^{c+d\,x}+1\right )}{2\,d}-\frac {\frac {4\,{\mathrm {e}}^{3\,c+3\,d\,x}\,\left (a-b\right )}{d}+\frac {4\,{\mathrm {e}}^{c+d\,x}\,\left (a+b\right )}{d}}{{\mathrm {e}}^{8\,c+8\,d\,x}-2\,{\mathrm {e}}^{4\,c+4\,d\,x}+1}-\frac {a\,\ln \left ({\mathrm {e}}^{c+d\,x}-1\right )}{2\,d}-\frac {\frac {{\mathrm {e}}^{3\,c+3\,d\,x}\,\left (a-b\right )}{d}+\frac {3\,{\mathrm {e}}^{c+d\,x}\,\left (a+b\right )}{d}}{{\mathrm {e}}^{4\,c+4\,d\,x}-1}-\frac {b\,\ln \left ({\mathrm {e}}^{c+d\,x}-\mathrm {i}\right )\,1{}\mathrm {i}}{2\,d}+\frac {b\,\ln \left ({\mathrm {e}}^{c+d\,x}+1{}\mathrm {i}\right )\,1{}\mathrm {i}}{2\,d} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*tanh(c + d*x)^3)/sinh(c + d*x)^3,x)

[Out]

(a*log(exp(c + d*x) + 1))/(2*d) - ((4*exp(3*c + 3*d*x)*(a - b))/d + (4*exp(c + d*x)*(a + b))/d)/(exp(8*c + 8*d
*x) - 2*exp(4*c + 4*d*x) + 1) - (a*log(exp(c + d*x) - 1))/(2*d) - ((exp(3*c + 3*d*x)*(a - b))/d + (3*exp(c + d
*x)*(a + b))/d)/(exp(4*c + 4*d*x) - 1) - (b*log(exp(c + d*x) - 1i)*1i)/(2*d) + (b*log(exp(c + d*x) + 1i)*1i)/(
2*d)

________________________________________________________________________________________