Optimal. Leaf size=11 \[ \frac {\sin ^4(x)}{4}+\sin (x) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {3223} \[ \frac {\sin ^4(x)}{4}+\sin (x) \]
Antiderivative was successfully verified.
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Rule 3223
Rubi steps
\begin {align*} \int \cos (x) \left (1+\sin ^3(x)\right ) \, dx &=\operatorname {Subst}\left (\int \left (1+x^3\right ) \, dx,x,\sin (x)\right )\\ &=\sin (x)+\frac {\sin ^4(x)}{4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {\sin ^4(x)}{4}+\sin (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 15, normalized size = 1.36 \[ \frac {1}{4} \, \cos \relax (x)^{4} - \frac {1}{2} \, \cos \relax (x)^{2} + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 9, normalized size = 0.82 \[ \frac {1}{4} \, \sin \relax (x)^{4} + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 10, normalized size = 0.91 \[ \frac {\left (\sin ^{4}\relax (x )\right )}{4}+\sin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 9, normalized size = 0.82 \[ \frac {1}{4} \, \sin \relax (x)^{4} + \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 9, normalized size = 0.82 \[ \frac {{\sin \relax (x)}^4}{4}+\sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.57, size = 8, normalized size = 0.73 \[ \frac {\sin ^{4}{\relax (x )}}{4} + \sin {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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