3.23 \(\int (e x)^m \sinh ^p(a+b x^2) \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left ((e x)^m \sinh ^p\left (a+b x^2\right ),x\right ) \]

[Out]

Unintegrable[(e*x)^m*Sinh[a + b*x^2]^p, x]

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Rubi [A]  time = 0.0196521, 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 = {} \[ \int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e*x)^m*Sinh[a + b*x^2]^p,x]

[Out]

Defer[Int][(e*x)^m*Sinh[a + b*x^2]^p, x]

Rubi steps

\begin{align*} \int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx &=\int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 2.3787, size = 0, normalized size = 0. \[ \int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e*x)^m*Sinh[a + b*x^2]^p,x]

[Out]

Integrate[(e*x)^m*Sinh[a + b*x^2]^p, x]

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Maple [A]  time = 0.039, size = 0, normalized size = 0. \begin{align*} \int \left ( ex \right ) ^{m} \left ( \sinh \left ( b{x}^{2}+a \right ) \right ) ^{p}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m*sinh(b*x^2+a)^p,x)

[Out]

int((e*x)^m*sinh(b*x^2+a)^p,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \sinh \left (b x^{2} + a\right )^{p}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sinh(b*x^2+a)^p,x, algorithm="maxima")

[Out]

integrate((e*x)^m*sinh(b*x^2 + a)^p, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sinh(b*x^2+a)^p,x, algorithm="fricas")

[Out]

integral((e*x)^m*sinh(b*x^2 + a)^p, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \sinh ^{p}{\left (a + b x^{2} \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)**m*sinh(b*x**2+a)**p,x)

[Out]

Integral((e*x)**m*sinh(a + b*x**2)**p, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sinh(b*x^2+a)^p,x, algorithm="giac")

[Out]

integrate((e*x)^m*sinh(b*x^2 + a)^p, x)