3.25 \(\int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{(b \tanh (e+f x))^{3/2}}{c+d x},x\right ) \]

[Out]

Unintegrable[(b*Tanh[e + f*x])^(3/2)/(c + d*x), x]

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Rubi [A]  time = 0.0686474, 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 = {} \[ \int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(b*Tanh[e + f*x])^(3/2)/(c + d*x),x]

[Out]

Defer[Int][(b*Tanh[e + f*x])^(3/2)/(c + d*x), x]

Rubi steps

\begin{align*} \int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx &=\int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx\\ \end{align*}

Mathematica [A]  time = 26.7531, size = 0, normalized size = 0. \[ \int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(b*Tanh[e + f*x])^(3/2)/(c + d*x),x]

[Out]

Integrate[(b*Tanh[e + f*x])^(3/2)/(c + d*x), x]

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Maple [A]  time = 0.089, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c} \left ( b\tanh \left ( fx+e \right ) \right ) ^{{\frac{3}{2}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*tanh(f*x+e))^(3/2)/(d*x+c),x)

[Out]

int((b*tanh(f*x+e))^(3/2)/(d*x+c),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b \tanh \left (f x + e\right )\right )^{\frac{3}{2}}}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(3/2)/(d*x+c),x, algorithm="maxima")

[Out]

integrate((b*tanh(f*x + e))^(3/2)/(d*x + c), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(3/2)/(d*x+c),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b \tanh{\left (e + f x \right )}\right )^{\frac{3}{2}}}{c + d x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))**(3/2)/(d*x+c),x)

[Out]

Integral((b*tanh(e + f*x))**(3/2)/(c + d*x), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (b \tanh \left (f x + e\right )\right )^{\frac{3}{2}}}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(3/2)/(d*x+c),x, algorithm="giac")

[Out]

integrate((b*tanh(f*x + e))^(3/2)/(d*x + c), x)