Optimal. Leaf size=7 \[ x \sin (x)+\cos (x) \]
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Rubi [A] time = 0.01, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {3296, 2638} \[ x \sin (x)+\cos (x) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3296
Rubi steps
\begin {align*} \int x \cos (x) \, dx &=x \sin (x)-\int \sin (x) \, dx\\ &=\cos (x)+x \sin (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 1.00 \[ x \sin (x)+\cos (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 7, normalized size = 1.00 \[ x \sin \relax (x) + \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 7, normalized size = 1.00 \[ x \sin \relax (x) + \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 1.14 \[ x \sin \relax (x )+\cos \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 7, normalized size = 1.00 \[ x \sin \relax (x) + \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 7, normalized size = 1.00 \[ \cos \relax (x)+x\,\sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 7, normalized size = 1.00 \[ x \sin {\relax (x )} + \cos {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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