3.100 \(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{S(b x) \cos \left (\frac{1}{2} \pi b^2 x^2\right )}{x},x\right ) \]

[Out]

Unintegrable[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x]

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Rubi [A]  time = 0.0178919, 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 = {} \[ \int \frac{\cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x,x]

[Out]

Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x]

Rubi steps

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

Mathematica [A]  time = 0.0304774, size = 0, normalized size = 0. \[ \int \frac{\cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x,x]

[Out]

Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x]

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Maple [A]  time = 0.086, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it FresnelS} \left ( bx \right ) }{x}\cos \left ({\frac{{b}^{2}\pi \,{x}^{2}}{2}} \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(1/2*b^2*Pi*x^2)*FresnelS(b*x)/x,x)

[Out]

int(cos(1/2*b^2*Pi*x^2)*FresnelS(b*x)/x,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(1/2*b^2*pi*x^2)*fresnels(b*x)/x,x, algorithm="maxima")

[Out]

integrate(cos(1/2*pi*b^2*x^2)*fresnels(b*x)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(1/2*b^2*pi*x^2)*fresnels(b*x)/x,x, algorithm="fricas")

[Out]

integral(cos(1/2*pi*b^2*x^2)*fresnels(b*x)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(1/2*b**2*pi*x**2)*fresnels(b*x)/x,x)

[Out]

Integral(cos(pi*b**2*x**2/2)*fresnels(b*x)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(1/2*b^2*pi*x^2)*fresnels(b*x)/x,x, algorithm="giac")

[Out]

integrate(cos(1/2*pi*b^2*x^2)*fresnels(b*x)/x, x)