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

Optimal. Leaf size=21 \[ \text{Unintegrable}\left (\sin \left (\frac{1}{2} \pi b^2 x^2\right ) \text{FresnelC}(b x)^n,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0129616, 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 = {} \[ \int \text{FresnelC}(b x)^n \sin \left (\frac{1}{2} b^2 \pi x^2\right ) \, dx \]

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*}

Mathematica [A]  time = 0.0690703, size = 0, normalized size = 0. \[ \int \text{FresnelC}(b x)^n \sin \left (\frac{1}{2} b^2 \pi x^2\right ) \, dx \]

Verification is Not applicable to the result.

[In]

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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Maple [A]  time = 0.059, size = 0, normalized size = 0. \begin{align*} \int \left ({\it FresnelC} \left ( bx \right ) \right ) ^{n}\sin \left ({\frac{{b}^{2}\pi \,{x}^{2}}{2}} \right ) \, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int{\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac{1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac{1}{2} \, \pi b^{2} x^{2}\right ), x\right ) \end{align*}

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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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sin{\left (\frac{\pi b^{2} x^{2}}{2} \right )} C^{n}\left (b x\right )\, dx \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm fresnelc}\left (b x\right )^{n} \sin \left (\frac{1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \end{align*}

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)