3.1.9 \(\int \frac {\tanh ^2(e+f x)}{c+d x} \, dx\) [9]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\tanh ^2(e+f x)}{c+d x},x\right ) \]

[Out]

Unintegrable(tanh(f*x+e)^2/(d*x+c),x)

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Rubi [A]
time = 0.02, 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 ^2(e+f x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Tanh[e + f*x]^2/(c + d*x),x]

[Out]

Defer[Int][Tanh[e + f*x]^2/(c + d*x), x]

Rubi steps

\begin {align*} \int \frac {\tanh ^2(e+f x)}{c+d x} \, dx &=\int \frac {\tanh ^2(e+f x)}{c+d x} \, dx\\ \end {align*}

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Mathematica [A]
time = 13.78, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^2(e+f x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Tanh[e + f*x]^2/(c + d*x),x]

[Out]

Integrate[Tanh[e + f*x]^2/(c + d*x), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\tanh ^{2}\left (f x +e \right )}{d x +c}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(f*x+e)^2/(d*x+c),x)

[Out]

int(tanh(f*x+e)^2/(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)^2/(d*x+c),x, algorithm="maxima")

[Out]

2*d*integrate(1/(d^2*f*x^2 + 2*c*d*f*x + c^2*f + (d^2*f*x^2*e^(2*e) + 2*c*d*f*x*e^(2*e) + c^2*f*e^(2*e))*e^(2*
f*x)), x) + log(d*x + c)/d + 2/(d*f*x + c*f + (d*f*x*e^(2*e) + c*f*e^(2*e))*e^(2*f*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)^2/(d*x+c),x, algorithm="fricas")

[Out]

integral(tanh(f*x + e)^2/(d*x + c), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^{2}{\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)**2/(d*x+c),x)

[Out]

Integral(tanh(e + f*x)**2/(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)^2/(d*x+c),x, algorithm="giac")

[Out]

integrate(tanh(f*x + e)^2/(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 )}^2}{c+d\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(e + f*x)^2/(c + d*x),x)

[Out]

int(tanh(e + f*x)^2/(c + d*x), x)

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