Optimal. Leaf size=6 \[ \frac{\sin (x)}{a^2} \]
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Rubi [A] time = 0.0385285, antiderivative size = 6, normalized size of antiderivative = 1., 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 3175
Rule 2637
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*}
Mathematica [A] time = 0.0017739, size = 6, normalized size = 1. \[ \frac{\sin (x)}{a^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.03, size = 7, normalized size = 1.2 \begin{align*}{\frac{\sin \left ( x \right ) }{{a}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.995567, size = 8, normalized size = 1.33 \begin{align*} \frac{\sin \left (x\right )}{a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78371, size = 16, normalized size = 2.67 \begin{align*} \frac{\sin \left (x\right )}{a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 30.1794, size = 19, normalized size = 3.17 \begin{align*} \frac{2 \tan{\left (\frac{x}{2} \right )}}{a^{2} \tan ^{2}{\left (\frac{x}{2} \right )} + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09659, size = 8, normalized size = 1.33 \begin{align*} \frac{\sin \left (x\right )}{a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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