3.9 \(\int \frac {\tanh ^2(e+f x)}{c+d x} \, dx\)

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 = 0.04, 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 = {} \[ \int \frac {\tanh ^2(e+f x)}{c+d x} \, dx \]

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 = 19.34, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^2(e+f x)}{c+d x} \, dx \]

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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fricas [A]  time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\tanh \left (f x + e\right )^{2}}{d x + c}, x\right ) \]

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

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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maple [A]  time = 0.24, 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 \[ 2 \, d \int \frac {1}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f + {\left (d^{2} f x^{2} e^{\left (2 \, e\right )} + 2 \, c d f x e^{\left (2 \, e\right )} + c^{2} f e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} + \frac {\log \left (d x + c\right )}{d} + \frac {2}{d f x + c f + {\left (d f x e^{\left (2 \, e\right )} + c f e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^2}{c+d\,x} \,d x \]

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

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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