Optimal. Leaf size=22 \[ \text {Int}\left (\cos \left (\frac {1}{2} \pi b^2 x^2\right ) S(b x)^n,x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \cos \left (\frac {1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx \]
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*}
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Mathematica [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int \cos \left (\frac {1}{2} b^2 \pi x^2\right ) S(b x)^n \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\rm fresnels}\left (b x\right )^{n} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnels}\left (b x\right )^{n} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 0, normalized size = 0.00 \[ \int \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right ) \mathrm {S}\left (b x \right )^{n}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnels}\left (b x\right )^{n} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int {\mathrm {FresnelS}\left (b\,x\right )}^n\,\cos \left (\frac {\Pi \,b^2\,x^2}{2}\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cos {\left (\frac {\pi b^{2} x^{2}}{2} \right )} S^{n}\left (b x\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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