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

Optimal. Leaf size=19 \[ \text {Int}\left ((e x)^m \sinh ^p\left (a+b x^2\right ),x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, 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 = {} \[ \int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx \]

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*}

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Mathematica [A]  time = 2.51, size = 0, normalized size = 0.00 \[ \int (e x)^m \sinh ^p\left (a+b x^2\right ) \, dx \]

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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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (e x\right )^{m} \sinh \left (b x^{2} + a\right )^{p}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sinh \left (b x^{2} + a\right )^{p}\,{d x} \]

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)

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maple [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \left (e x \right )^{m} \left (\sinh ^{p}\left (b \,x^{2}+a \right )\right )\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sinh \left (b x^{2} + a\right )^{p}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int {\mathrm {sinh}\left (b\,x^2+a\right )}^p\,{\left (e\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinh(a + b*x^2)^p*(e*x)^m,x)

[Out]

int(sinh(a + b*x^2)^p*(e*x)^m, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sinh ^{p}{\left (a + b x^{2} \right )}\, dx \]

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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