3.427 \(\int (a+b \sin ^4(e+f x))^p \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\left (a+b \sin ^4(e+f x)\right )^p,x\right ) \]

[Out]

Unintegrable((a+b*sin(f*x+e)^4)^p,x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \left (a+b \sin ^4(e+f x)\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + b*Sin[e + f*x]^4)^p,x]

[Out]

Defer[Int][(a + b*Sin[e + f*x]^4)^p, x]

Rubi steps

\begin {align*} \int \left (a+b \sin ^4(e+f x)\right )^p \, dx &=\int \left (a+b \sin ^4(e+f x)\right )^p \, dx\\ \end {align*}

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Mathematica [A]  time = 1.13, size = 0, normalized size = 0.00 \[ \int \left (a+b \sin ^4(e+f x)\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + b*Sin[e + f*x]^4)^p,x]

[Out]

Integrate[(a + b*Sin[e + f*x]^4)^p, x]

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fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \cos \left (f x + e\right )^{4} - 2 \, b \cos \left (f x + e\right )^{2} + a + b\right )}^{p}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sin(f*x+e)^4)^p,x, algorithm="fricas")

[Out]

integral((b*cos(f*x + e)^4 - 2*b*cos(f*x + e)^2 + a + b)^p, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \sin \left (f x + e\right )^{4} + a\right )}^{p}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sin(f*x+e)^4)^p,x, algorithm="giac")

[Out]

integrate((b*sin(f*x + e)^4 + a)^p, x)

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maple [A]  time = 2.14, size = 0, normalized size = 0.00 \[ \int \left (a +b \left (\sin ^{4}\left (f x +e \right )\right )\right )^{p}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*sin(f*x+e)^4)^p,x)

[Out]

int((a+b*sin(f*x+e)^4)^p,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \sin \left (f x + e\right )^{4} + a\right )}^{p}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sin(f*x+e)^4)^p,x, algorithm="maxima")

[Out]

integrate((b*sin(f*x + e)^4 + a)^p, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int {\left (b\,{\sin \left (e+f\,x\right )}^4+a\right )}^p \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*sin(e + f*x)^4)^p,x)

[Out]

int((a + b*sin(e + f*x)^4)^p, x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*sin(f*x+e)**4)**p,x)

[Out]

Timed out

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