Optimal. Leaf size=10 \[ \frac {\text {Si}(b x)^2}{2} \]
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Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, 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*}
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Mathematica [C] time = 0.02, size = 26, normalized size = 2.60 \[ \frac {\text {Si}(b x)^2 \sin (b x)}{2 b x \text {sinc}(b x)} \]
Warning: Unable to verify antiderivative.
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fricas [F] time = 3.60, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (b x\right ) \operatorname {Si}\left (b x\right )}{x}, x\right ) \]
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 \[ \int \frac {{\rm Si}\left (b x\right ) \sin \left (b x\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 9, normalized size = 0.90 \[ \frac {\Si \left (b x \right )^{2}}{2} \]
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 \[ \int \frac {{\rm Si}\left (b x\right ) \sin \left (b x\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.10 \[ \frac {{\mathrm {sinint}\left (b\,x\right )}^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.72, size = 7, normalized size = 0.70 \[ \frac {\operatorname {Si}^{2}{\left (b x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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