3.309 \(\int (e+f x)^m (a+b \sin (c+\frac{d}{x}))^p \, dx\)

Optimal. Leaf size=24 \[ \text{Unintegrable}\left ((e+f x)^m \left (a+b \sin \left (c+\frac{d}{x}\right )\right )^p,x\right ) \]

[Out]

Unintegrable[(e + f*x)^m*(a + b*Sin[c + d/x])^p, x]

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Rubi [A]  time = 0.0279417, 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 = {} \[ \int (e+f x)^m \left (a+b \sin \left (c+\frac{d}{x}\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e + f*x)^m*(a + b*Sin[c + d/x])^p,x]

[Out]

Defer[Int][(e + f*x)^m*(a + b*Sin[c + d/x])^p, x]

Rubi steps

\begin{align*} \int (e+f x)^m \left (a+b \sin \left (c+\frac{d}{x}\right )\right )^p \, dx &=\int (e+f x)^m \left (a+b \sin \left (c+\frac{d}{x}\right )\right )^p \, dx\\ \end{align*}

Mathematica [A]  time = 1.39924, size = 0, normalized size = 0. \[ \int (e+f x)^m \left (a+b \sin \left (c+\frac{d}{x}\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e + f*x)^m*(a + b*Sin[c + d/x])^p,x]

[Out]

Integrate[(e + f*x)^m*(a + b*Sin[c + d/x])^p, x]

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Maple [A]  time = 0.513, size = 0, normalized size = 0. \begin{align*} \int \left ( fx+e \right ) ^{m} \left ( a+b\sin \left ( c+{\frac{d}{x}} \right ) \right ) ^{p}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f*x+e)^m*(a+b*sin(c+d/x))^p,x)

[Out]

int((f*x+e)^m*(a+b*sin(c+d/x))^p,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x+e)^m*(a+b*sin(c+d/x))^p,x, algorithm="maxima")

[Out]

integrate((f*x + e)^m*(b*sin(c + d/x) + a)^p, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x+e)^m*(a+b*sin(c+d/x))^p,x, algorithm="fricas")

[Out]

integral((f*x + e)^m*(b*sin((c*x + d)/x) + a)^p, 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((f*x+e)**m*(a+b*sin(c+d/x))**p,x)

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x+e)^m*(a+b*sin(c+d/x))^p,x, algorithm="giac")

[Out]

integrate((f*x + e)^m*(b*sin(c + d/x) + a)^p, x)