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 = 0.0112121, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, 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 3296
Rule 2637
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*}
Mathematica [A] time = 0.0105456, 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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Maple [A] time = 0.006, size = 21, normalized size = 1. \begin{align*} -{\frac{2\,\cos \left ( 5\,x \right ) }{5}}+{\frac{3\,\sin \left ( 5\,x \right ) }{25}}-{\frac{3\,\cos \left ( 5\,x \right ) x}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946682, size = 27, normalized size = 1.23 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.447508, size = 55, normalized size = 2.5 \begin{align*} -\frac{1}{5} \,{\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac{3}{25} \, \sin \left (5 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.171743, size = 26, normalized size = 1.18 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08561, size = 24, normalized size = 1.09 \begin{align*} -\frac{1}{5} \,{\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac{3}{25} \, \sin \left (5 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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