3.14 \(\int \frac{\tanh ^3(e+f x)}{c+d x} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\tanh ^3(e+f x)}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0377008, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\tanh ^3(e+f x)}{c+d x} \, dx \]

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*}

Mathematica [A]  time = 30.2242, size = 0, normalized size = 0. \[ \int \frac{\tanh ^3(e+f x)}{c+d x} \, dx \]

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 = 0.388, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \tanh \left ( fx+e \right ) \right ) ^{3}}{dx+c}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \frac{{\left (2 \, d f x e^{\left (2 \, e\right )} + 2 \, c f e^{\left (2 \, e\right )} - d e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )} - d}{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} +{\left (d^{2} f^{2} x^{2} e^{\left (4 \, e\right )} + 2 \, c d f^{2} x e^{\left (4 \, e\right )} + c^{2} f^{2} e^{\left (4 \, e\right )}\right )} e^{\left (4 \, f x\right )} + 2 \,{\left (d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 2 \, c d f^{2} x e^{\left (2 \, e\right )} + c^{2} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} + \frac{\log \left (d x + c\right )}{d} - \int \frac{2 \,{\left (d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + d^{2}\right )}}{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} +{\left (d^{3} f^{2} x^{3} e^{\left (2 \, e\right )} + 3 \, c d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 3 \, c^{2} d f^{2} x e^{\left (2 \, e\right )} + c^{3} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} \end{align*}

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*e^(2*e) - 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., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\tanh \left (f x + e\right )^{3}}{d x + c}, x\right ) \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{\tanh ^{3}{\left (e + f x \right )}}{c + d x}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{\tanh \left (f x + e\right )^{3}}{d x + c}\,{d x} \end{align*}

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)