Optimal. Leaf size=12 \[ \sin (a+x)-x \cos (a+x) \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 2637
Rule 3296
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*}
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Mathematica [A] time = 0.03, size = 12, normalized size = 1.00 \[ \sin (a+x)-x \cos (a+x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 12, normalized size = 1.00 \[ -x \cos \left (a + x\right ) + \sin \left (a + x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.33, size = 12, normalized size = 1.00 \[ -x \cos \left (a + x\right ) + \sin \left (a + x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 1.75 \[ a \cos \left (a +x \right )-\left (a +x \right ) \cos \left (a +x \right )+\sin \left (a +x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 20, normalized size = 1.67 \[ -{\left (a + x\right )} \cos \left (a + x\right ) + a \cos \left (a + x\right ) + \sin \left (a + x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 12, normalized size = 1.00 \[ \sin \left (a+x\right )-x\,\cos \left (a+x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 10, normalized size = 0.83 \[ - x \cos {\left (a + x \right )} + \sin {\left (a + x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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