Optimal. Leaf size=29 \[ -\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10}-\frac {1}{5} \text {Si}(2 x) \cos (5 x) \]
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Rubi [A] time = 0.06, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.444, Rules used = {6511, 12, 4430, 3299} \[ -\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10}-\frac {1}{5} \text {Si}(2 x) \cos (5 x) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3299
Rule 4430
Rule 6511
Rubi steps
\begin {align*} \int \sin (5 x) \text {Si}(2 x) \, dx &=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {2}{5} \int \frac {\cos (5 x) \sin (2 x)}{2 x} \, dx\\ &=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {1}{5} \int \frac {\cos (5 x) \sin (2 x)}{x} \, dx\\ &=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)+\frac {1}{5} \int \left (-\frac {\sin (3 x)}{2 x}+\frac {\sin (7 x)}{2 x}\right ) \, dx\\ &=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)-\frac {1}{10} \int \frac {\sin (3 x)}{x} \, dx+\frac {1}{10} \int \frac {\sin (7 x)}{x} \, dx\\ &=-\frac {1}{5} \cos (5 x) \text {Si}(2 x)-\frac {\text {Si}(3 x)}{10}+\frac {\text {Si}(7 x)}{10}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 25, normalized size = 0.86 \[ \frac {1}{10} (-\text {Si}(3 x)+\text {Si}(7 x)-2 \text {Si}(2 x) \cos (5 x)) \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 23, normalized size = 0.79 \[ -\frac {1}{5} \, \cos \left (5 \, x\right ) \operatorname {Si}\left (2 \, x\right ) + \frac {1}{10} \, \operatorname {Si}\left (7 \, x\right ) - \frac {1}{10} \, \operatorname {Si}\left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 24, normalized size = 0.83 \[ -\frac {\cos \left (5 x \right ) \Si \left (2 x \right )}{5}-\frac {\Si \left (3 x \right )}{10}+\frac {\Si \left (7 x \right )}{10} \]
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 \[ \int {\rm Si}\left (2 \, x\right ) \sin \left (5 \, x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \mathrm {sinint}\left (2\,x\right )\,\sin \left (5\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sin {\left (5 x \right )} \operatorname {Si}{\left (2 x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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