Optimal. Leaf size=22 \[ \frac {3}{25} \sin (5 x)-\frac {1}{5} (3 x+2) \cos (5 x) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {3296, 2637} \[ \frac {3}{25} \sin (5 x)-\frac {1}{5} (3 x+2) \cos (5 x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3296
Rubi steps
\begin {align*} \int (2+3 x) \sin (5 x) \, dx &=-\frac {1}{5} (2+3 x) \cos (5 x)+\frac {3}{5} \int \cos (5 x) \, dx\\ &=-\frac {1}{5} (2+3 x) \cos (5 x)+\frac {3}{25} \sin (5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.18 \[ \frac {3}{25} \sin (5 x)-\frac {3}{5} x \cos (5 x)-\frac {2}{5} \cos (5 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 18, normalized size = 0.82 \[ -\frac {1}{5} \, {\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac {3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 18, normalized size = 0.82 \[ -\frac {1}{5} \, {\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac {3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.95 \[ -\frac {3 x \cos \left (5 x \right )}{5}-\frac {2 \cos \left (5 x \right )}{5}+\frac {3 \sin \left (5 x \right )}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 20, normalized size = 0.91 \[ -\frac {3}{5} \, x \cos \left (5 \, x\right ) - \frac {2}{5} \, \cos \left (5 \, x\right ) + \frac {3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 20, normalized size = 0.91 \[ \frac {3\,\sin \left (5\,x\right )}{25}-\frac {2\,\cos \left (5\,x\right )}{5}-\frac {3\,x\,\cos \left (5\,x\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 26, normalized size = 1.18 \[ - \frac {3 x \cos {\left (5 x \right )}}{5} + \frac {3 \sin {\left (5 x \right )}}{25} - \frac {2 \cos {\left (5 x \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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