3.1.14 \(\int \frac {\tanh ^3(e+f x)}{c+d x} \, dx\) [14]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\tanh ^3(e+f x)}{c+d x},x\right ) \]

[Out]

Unintegrable(tanh(f*x+e)^3/(d*x+c),x)

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Rubi [A]
time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Tanh[e + f*x]^3/(c + d*x),x]

[Out]

Defer[Int][Tanh[e + f*x]^3/(c + d*x), x]

Rubi steps

\begin {align*} \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx &=\int \frac {\tanh ^3(e+f x)}{c+d x} \, dx\\ \end {align*}

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Mathematica [A]
time = 21.78, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Tanh[e + f*x]^3/(c + d*x),x]

[Out]

Integrate[Tanh[e + f*x]^3/(c + d*x), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\tanh ^{3}\left (f x +e \right )}{d x +c}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(f*x+e)^3/(d*x+c),x)

[Out]

int(tanh(f*x+e)^3/(d*x+c),x)

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Maxima [A]
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(tanh(f*x+e)^3/(d*x+c),x, algorithm="maxima")

[Out]

((2*d*f*x*e^(2*e) + (2*c*f - d)*e^(2*e))*e^(2*f*x) - d)/(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + (d^2*f^2*x^2*e^
(4*e) + 2*c*d*f^2*x*e^(4*e) + c^2*f^2*e^(4*e))*e^(4*f*x) + 2*(d^2*f^2*x^2*e^(2*e) + 2*c*d*f^2*x*e^(2*e) + c^2*
f^2*e^(2*e))*e^(2*f*x)) + log(d*x + c)/d - integrate(2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + d^2)/(d^3*f^2*x^
3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 + (d^3*f^2*x^3*e^(2*e) + 3*c*d^2*f^2*x^2*e^(2*e) + 3*c^2*d*f^2*x
*e^(2*e) + c^3*f^2*e^(2*e))*e^(2*f*x)), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^3/(d*x+c),x, algorithm="fricas")

[Out]

integral(tanh(f*x + e)^3/(d*x + c), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^{3}{\left (e + f x \right )}}{c + d x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)**3/(d*x+c),x)

[Out]

Integral(tanh(e + f*x)**3/(c + d*x), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^3/(d*x+c),x, algorithm="giac")

[Out]

integrate(tanh(f*x + e)^3/(d*x + c), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^3}{c+d\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(e + f*x)^3/(c + d*x),x)

[Out]

int(tanh(e + f*x)^3/(c + d*x), x)

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