Optimal. Leaf size=9 \[ -\frac {\cos \left (x^n\right )}{n} \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {3379, 2638} \[ -\frac {\cos \left (x^n\right )}{n} \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3379
Rubi steps
\begin {align*} \int x^{-1+n} \sin \left (x^n\right ) \, dx &=\frac {\operatorname {Subst}\left (\int \sin (x) \, dx,x,x^n\right )}{n}\\ &=-\frac {\cos \left (x^n\right )}{n}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 9, normalized size = 1.00 \[ -\frac {\cos \left (x^n\right )}{n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 9, normalized size = 1.00 \[ -\frac {\cos \left (x^{n}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 9, normalized size = 1.00 \[ -\frac {\cos \left (x^{n}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 1.11 \[ -\frac {\cos \left (x^{n}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 9, normalized size = 1.00 \[ -\frac {\cos \left (x^{n}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 9, normalized size = 1.00 \[ -\frac {\cos \left (x^n\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 6.73, size = 7, normalized size = 0.78 \[ - \frac {\cos {\left (x^{n} \right )}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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