Optimal. Leaf size=49 \[ -\frac {\sin ^2(b x)}{x}-\frac {\sin (b x) \text {Si}(b x)}{x}+b \text {Si}(2 b x)+b \text {Int}\left (\frac {\cos (b x) \text {Si}(b x)}{x},x\right ) \]
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Rubi [A]
time = 0.11, 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 = {}
\begin {gather*} \int \frac {\sin (b x) \text {Si}(b x)}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sin (b x) \text {Si}(b x)}{x^2} \, dx &=-\frac {\sin (b x) \text {Si}(b x)}{x}+b \int \frac {\sin ^2(b x)}{b x^2} \, dx+b \int \frac {\cos (b x) \text {Si}(b x)}{x} \, dx\\ &=-\frac {\sin (b x) \text {Si}(b x)}{x}+b \int \frac {\cos (b x) \text {Si}(b x)}{x} \, dx+\int \frac {\sin ^2(b x)}{x^2} \, dx\\ &=-\frac {\sin ^2(b x)}{x}-\frac {\sin (b x) \text {Si}(b x)}{x}+b \int \frac {\cos (b x) \text {Si}(b x)}{x} \, dx+(2 b) \int \frac {\sin (2 b x)}{2 x} \, dx\\ &=-\frac {\sin ^2(b x)}{x}-\frac {\sin (b x) \text {Si}(b x)}{x}+b \int \frac {\sin (2 b x)}{x} \, dx+b \int \frac {\cos (b x) \text {Si}(b x)}{x} \, dx\\ &=-\frac {\sin ^2(b x)}{x}-\frac {\sin (b x) \text {Si}(b x)}{x}+b \text {Si}(2 b x)+b \int \frac {\cos (b x) \text {Si}(b x)}{x} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.58, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sin (b x) \text {Si}(b x)}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\sinIntegral \left (b x \right ) \sin \left (b x \right )}{x^{2}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\sin {\left (b x \right )} \operatorname {Si}{\left (b x \right )}}{x^{2}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int \frac {\mathrm {sinint}\left (b\,x\right )\,\sin \left (b\,x\right )}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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