Optimal. Leaf size=6 \[ \frac {\sin (x)}{a^2} \]
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Rubi [A] time = 0.04, antiderivative size = 6, 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, 2637} \[ \frac {\sin (x)}{a^2} \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3175
Rubi steps
\begin {align*} \int \frac {\cos ^5(x)}{\left (a-a \sin ^2(x)\right )^2} \, dx &=\frac {\int \cos (x) \, dx}{a^2}\\ &=\frac {\sin (x)}{a^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 1.00 \[ \frac {\sin (x)}{a^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 6, normalized size = 1.00 \[ \frac {\sin \relax (x)}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 6, normalized size = 1.00 \[ \frac {\sin \relax (x)}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 7, normalized size = 1.17 \[ \frac {\sin \relax (x )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 6, normalized size = 1.00 \[ \frac {\sin \relax (x)}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 6, normalized size = 1.00 \[ \frac {\sin \relax (x)}{a^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 19.21, size = 19, normalized size = 3.17 \[ \frac {2 \tan {\left (\frac {x}{2} \right )}}{a^{2} \tan ^{2}{\left (\frac {x}{2} \right )} + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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