Optimal. Leaf size=26 \[ \frac {\cos \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b}+x S(b x) \]
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Rubi [A] time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {6418} \[ \frac {\cos \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b}+x S(b x) \]
Antiderivative was successfully verified.
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Rule 6418
Rubi steps
\begin {align*} \int S(b x) \, dx &=\frac {\cos \left (\frac {1}{2} b^2 \pi x^2\right )}{b \pi }+x S(b x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 26, normalized size = 1.00 \[ \frac {\cos \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b}+x S(b x) \]
Antiderivative was successfully verified.
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fricas [F] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\rm fresnels}\left (b x\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnels}\left (b x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 27, normalized size = 1.04 \[ \frac {b x \,\mathrm {S}\left (b x \right )+\frac {\cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{\pi }}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnels}\left (b x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \mathrm {FresnelS}\left (b\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.74, size = 48, normalized size = 1.85 \[ \frac {3 x S\left (b x\right ) \Gamma \left (\frac {3}{4}\right )}{4 \Gamma \left (\frac {7}{4}\right )} + \frac {3 \cos {\left (\frac {\pi b^{2} x^{2}}{2} \right )} \Gamma \left (\frac {3}{4}\right )}{4 \pi b \Gamma \left (\frac {7}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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