Optimal. Leaf size=8 \[ -x \cos (x)+\sin (x) \]
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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 = {3377, 2717}
\begin {gather*} \sin (x)-x \cos (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2717
Rule 3377
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 \begin {gather*} -x \cos (x)+\sin (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 9, normalized size = 1.12
method | result | size |
default | \(-x \cos \left (x \right )+\sin \left (x \right )\) | \(9\) |
risch | \(-x \cos \left (x \right )+\sin \left (x \right )\) | \(9\) |
meijerg | \(2 \sqrt {\pi }\, \left (-\frac {x \cos \left (x \right )}{2 \sqrt {\pi }}+\frac {\sin \left (x \right )}{2 \sqrt {\pi }}\right )\) | \(22\) |
norman | \(\frac {x \left (\tan ^{2}\left (\frac {x}{2}\right )\right )-x +2 \tan \left (\frac {x}{2}\right )}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 3.61, size = 8, normalized size = 1.00 \begin {gather*} -x \cos \left (x\right ) + \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 8, normalized size = 1.00 \begin {gather*} -x \cos \left (x\right ) + \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 7, normalized size = 0.88 \begin {gather*} - x \cos {\left (x \right )} + \sin {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 8, normalized size = 1.00 \begin {gather*} -x \cos \left (x\right ) + \sin \left (x\right ) \end {gather*}
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 \begin {gather*} \sin \left (x\right )-x\,\cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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