Optimal. Leaf size=7 \[ -\frac {\cos (x)}{a} \]
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Rubi [A] time = 0.04, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {3175, 2638} \[ -\frac {\cos (x)}{a} \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3175
Rubi steps
\begin {align*} \int \frac {\sin ^3(x)}{a-a \cos ^2(x)} \, dx &=\frac {\int \sin (x) \, dx}{a}\\ &=-\frac {\cos (x)}{a}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 1.00 \[ -\frac {\cos (x)}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 7, normalized size = 1.00 \[ -\frac {\cos \relax (x)}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 7, normalized size = 1.00 \[ -\frac {\cos \relax (x)}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 8, normalized size = 1.14 \[ -\frac {\cos \relax (x )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 7, normalized size = 1.00 \[ -\frac {\cos \relax (x)}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 1.00 \[ -\frac {\cos \relax (x)}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.24, size = 12, normalized size = 1.71 \[ - \frac {2}{a \tan ^{2}{\left (\frac {x}{2} \right )} + a} \]
Verification of antiderivative is not currently implemented for this CAS.
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