Optimal. Leaf size=10 \[ \frac{\text{Si}(b x)^2}{2} \]
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Rubi [A] time = 0.020708, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {6686} \[ \frac{\text{Si}(b x)^2}{2} \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin{align*} \int \frac{\sin (b x) \text{Si}(b x)}{x} \, dx &=\frac{\text{Si}(b x)^2}{2}\\ \end{align*}
Mathematica [C] time = 0.0142256, size = 26, normalized size = 2.6 \[ \frac{\text{Si}(b x)^2 \sin (b x)}{2 b x \text{sinc}(b x)} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.041, size = 9, normalized size = 0.9 \begin{align*}{\frac{ \left ({\it Si} \left ( bx \right ) \right ) ^{2}}{2}} \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 Si}\left (b x\right ) \sin \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{\sin \left (b x\right ) \operatorname{Si}\left (b x\right )}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.06016, size = 7, normalized size = 0.7 \begin{align*} \frac{\operatorname{Si}^{2}{\left (b x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14573, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \operatorname{Si}\left (b x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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