3.199 \(\int C(b x)^n \sin (\frac {1}{2} b^2 \pi x^2) \, dx\)

Optimal. Leaf size=22 \[ \text {Int}\left (\sin \left (\frac {1}{2} \pi b^2 x^2\right ) C(b x)^n,x\right ) \]

[Out]

Unintegrable(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),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 = {} \[ \int \text {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]

[Out]

Defer[Int][FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]

Rubi steps

\begin {align*} \int C(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx &=\int C(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx\\ \end {align*}

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Mathematica [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int C(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]

[Out]

Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]

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fricas [A]  time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="fricas")

[Out]

integral(fresnelc(b*x)^n*sin(1/2*pi*b^2*x^2), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="giac")

[Out]

integrate(fresnelc(b*x)^n*sin(1/2*pi*b^2*x^2), x)

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \FresnelC \left (b x \right )^{n} \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),x)

[Out]

int(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="maxima")

[Out]

integrate(fresnelc(b*x)^n*sin(1/2*pi*b^2*x^2), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int {\mathrm {FresnelC}\left (b\,x\right )}^n\,\sin \left (\frac {\Pi \,b^2\,x^2}{2}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(FresnelC(b*x)^n*sin((Pi*b^2*x^2)/2),x)

[Out]

int(FresnelC(b*x)^n*sin((Pi*b^2*x^2)/2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sin {\left (\frac {\pi b^{2} x^{2}}{2} \right )} C^{n}\left (b x\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)**n*sin(1/2*b**2*pi*x**2),x)

[Out]

Integral(sin(pi*b**2*x**2/2)*fresnelc(b*x)**n, x)

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