Optimal. Leaf size=8 \[ \sin (x)-x \cos (x) \]
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Rubi [A] time = 0.01, antiderivative size = 8, 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, 2637} \[ \sin (x)-x \cos (x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3296
Rubi steps
\begin {align*} \int x \sin (x) \, dx &=-x \cos (x)+\int \cos (x) \, dx\\ &=-x \cos (x)+\sin (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \sin (x)-x \cos (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 8, normalized size = 1.00 \[ -x \cos \relax (x) + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 8, normalized size = 1.00 \[ -x \cos \relax (x) + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 1.12 \[ -x \cos \relax (x )+\sin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 8, normalized size = 1.00 \[ -x \cos \relax (x) + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 8, normalized size = 1.00 \[ \sin \relax (x)-x\,\cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 7, normalized size = 0.88 \[ - x \cos {\relax (x )} + \sin {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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