Optimal. Leaf size=21 \[ \text{Unintegrable}\left (\cos \left (\frac{1}{2} \pi b^2 x^2\right ) S(b x)^n,x\right ) \]
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Rubi [A] time = 0.0146736, 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 = {} \[ \int \cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx &=\int \cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx\\ \end{align*}
Mathematica [A] time = 0.0730368, size = 0, normalized size = 0. \[ \int \cos \left (\frac{1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.062, size = 0, normalized size = 0. \begin{align*} \int \cos \left ({\frac{{b}^{2}\pi \,{x}^{2}}{2}} \right ) \left ({\it FresnelS} \left ( bx \right ) \right ) ^{n}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm fresnels}\left (b x\right )^{n} \cos \left (\frac{1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\rm fresnels}\left (b x\right )^{n} \cos \left (\frac{1}{2} \, \pi b^{2} x^{2}\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \cos{\left (\frac{\pi b^{2} x^{2}}{2} \right )} S^{n}\left (b x\right )\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm fresnels}\left (b x\right )^{n} \cos \left (\frac{1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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