3.48 \(\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left ((c+d x)^m (a \tanh (e+f x)+a)^2,x\right ) \]

[Out]

Unintegrable[(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]

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Rubi [A]  time = 0.0497497, 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 = {} \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 22.2301, size = 0, normalized size = 0. \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.083, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( a+a\tanh \left ( fx+e \right ) \right ) ^{2}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (a^{2} \tanh \left (f x + e\right )^{2} + 2 \, a^{2} \tanh \left (f x + e\right ) + a^{2}\right )}{\left (d x + c\right )}^{m}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="fricas")

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**m*(a+a*tanh(f*x+e))**2,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (a \tanh \left (f x + e\right ) + a\right )}^{2}{\left (d x + c\right )}^{m}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="giac")

[Out]

integrate((a*tanh(f*x + e) + a)^2*(d*x + c)^m, x)