3.3.87 \(\int (e x)^m (a+b \sin (c+d (f+g x)^n))^p \, dx\) [287]

Optimal. Leaf size=27 \[ \text {Int}\left ((e x)^m \left (a+b \sin \left (c+d (f+g x)^n\right )\right )^p,x\right ) \]

[Out]

Unintegrable((e*x)^m*(a+b*sin(c+d*(g*x+f)^n))^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 = {} \begin {gather*} \int (e x)^m \left (a+b \sin \left (c+d (f+g x)^n\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 1.40, size = 0, normalized size = 0.00 \begin {gather*} \int (e x)^m \left (a+b \sin \left (c+d (f+g x)^n\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \left (e x \right )^{m} \left (a +b \sin \left (c +d \left (g x +f \right )^{n}\right )\right )^{p}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\left (e\,x\right )}^m\,{\left (a+b\,\sin \left (c+d\,{\left (f+g\,x\right )}^n\right )\right )}^p \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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