Optimal. Leaf size=69 \[ \frac{1}{2} b x \text{HypergeometricPFQ}\left (\left \{\frac{1}{2},\frac{1}{2}\right \},\left \{\frac{3}{2},\frac{3}{2}\right \},-\frac{1}{2} i \pi b^2 x^2\right )+\frac{1}{2} b x \text{HypergeometricPFQ}\left (\left \{\frac{1}{2},\frac{1}{2}\right \},\left \{\frac{3}{2},\frac{3}{2}\right \},\frac{1}{2} i \pi b^2 x^2\right ) \]
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Rubi [A] time = 0.0443547, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {6425, 6358, 6360} \[ \frac{1}{2} b x \, _2F_2\left (\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{1}{2} i b^2 \pi x^2\right )+\frac{1}{2} b x \, _2F_2\left (\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{1}{2} i b^2 \pi x^2\right ) \]
Antiderivative was successfully verified.
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Rule 6425
Rule 6358
Rule 6360
Rubi steps
\begin{align*} \int \frac{C(b x)}{x} \, dx &=\left (\frac{1}{4}-\frac{i}{4}\right ) \int \frac{\text{erf}\left (\left (\frac{1}{2}+\frac{i}{2}\right ) b \sqrt{\pi } x\right )}{x} \, dx+\left (\frac{1}{4}-\frac{i}{4}\right ) \int \frac{\text{erfi}\left (\left (\frac{1}{2}+\frac{i}{2}\right ) b \sqrt{\pi } x\right )}{x} \, dx\\ &=\frac{1}{2} b x \, _2F_2\left (\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{1}{2} i b^2 \pi x^2\right )+\frac{1}{2} b x \, _2F_2\left (\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{1}{2} i b^2 \pi x^2\right )\\ \end{align*}
Mathematica [F] time = 0.0140928, size = 0, normalized size = 0. \[ \int \frac{\text{FresnelC}(b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.073, size = 23, normalized size = 0.3 \begin{align*} bx{\mbox{$_2$F$_3$}({\frac{1}{4}},{\frac{1}{4}};\,{\frac{1}{2}},{\frac{5}{4}},{\frac{5}{4}};\,-{\frac{{x}^{4}{\pi }^{2}{b}^{4}}{16}})} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnelc}\left (b x\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\rm fresnelc}\left (b x\right )}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: AttributeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnelc}\left (b x\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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