Optimal. Leaf size=18 \[ \frac {x \sin (\pi x)}{\pi }+\frac {\cos (\pi x)}{\pi ^2} \]
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Rubi [A] time = 0.01, antiderivative size = 18, 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, 2638} \[ \frac {x \sin (\pi x)}{\pi }+\frac {\cos (\pi x)}{\pi ^2} \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3296
Rubi steps
\begin {align*} \int x \cos (\pi x) \, dx &=\frac {x \sin (\pi x)}{\pi }-\frac {\int \sin (\pi x) \, dx}{\pi }\\ &=\frac {\cos (\pi x)}{\pi ^2}+\frac {x \sin (\pi x)}{\pi }\\ \end {align*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 1.00 \[ \frac {x \sin (\pi x)}{\pi }+\frac {\cos (\pi x)}{\pi ^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 16, normalized size = 0.89 \[ \frac {\pi x \sin \left (\pi x\right ) + \cos \left (\pi x\right )}{\pi ^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 18, normalized size = 1.00 \[ \frac {x \sin \left (\pi x\right )}{\pi } + \frac {\cos \left (\pi x\right )}{\pi ^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.94 \[ \frac {\pi x \sin \left (\pi x \right )+\cos \left (\pi x \right )}{\pi ^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 16, normalized size = 0.89 \[ \frac {\pi x \sin \left (\pi x\right ) + \cos \left (\pi x\right )}{\pi ^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 16, normalized size = 0.89 \[ \frac {\cos \left (\Pi \,x\right )+\Pi \,x\,\sin \left (\Pi \,x\right )}{\Pi ^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 15, normalized size = 0.83 \[ \frac {x \sin {\left (\pi x \right )}}{\pi } + \frac {\cos {\left (\pi x \right )}}{\pi ^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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