Optimal. Leaf size=12 \[ \sin (a+x)-x \cos (a+x) \]
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Rubi [A] time = 0.0092589, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {3296, 2637} \[ \sin (a+x)-x \cos (a+x) \]
Antiderivative was successfully verified.
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Rule 3296
Rule 2637
Rubi steps
\begin{align*} \int x \sin (a+x) \, dx &=-x \cos (a+x)+\int \cos (a+x) \, dx\\ &=-x \cos (a+x)+\sin (a+x)\\ \end{align*}
Mathematica [A] time = 0.0242601, size = 12, normalized size = 1. \[ \sin (a+x)-x \cos (a+x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 21, normalized size = 1.8 \begin{align*} a\cos \left ( a+x \right ) +\sin \left ( a+x \right ) - \left ( a+x \right ) \cos \left ( a+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943976, size = 27, normalized size = 2.25 \begin{align*} -{\left (a + x\right )} \cos \left (a + x\right ) + a \cos \left (a + x\right ) + \sin \left (a + x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68374, size = 38, normalized size = 3.17 \begin{align*} -x \cos \left (a + x\right ) + \sin \left (a + x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.168637, size = 10, normalized size = 0.83 \begin{align*} - x \cos{\left (a + x \right )} + \sin{\left (a + x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09323, size = 16, normalized size = 1.33 \begin{align*} -x \cos \left (a + x\right ) + \sin \left (a + x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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