Optimal. Leaf size=5 \[ \frac{x}{a} \]
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Rubi [A] time = 0.040586, antiderivative size = 5, 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, 8} \[ \frac{x}{a} \]
Antiderivative was successfully verified.
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Rule 3175
Rule 8
Rubi steps
\begin{align*} \int \frac{\cos ^2(x)}{a-a \sin ^2(x)} \, dx &=\frac{\int 1 \, dx}{a}\\ &=\frac{x}{a}\\ \end{align*}
Mathematica [A] time = 0.0007805, size = 5, normalized size = 1. \[ \frac{x}{a} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.033, size = 8, normalized size = 1.6 \begin{align*}{\frac{\arctan \left ( \tan \left ( x \right ) \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.47286, size = 7, normalized size = 1.4 \begin{align*} \frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58364, size = 7, normalized size = 1.4 \begin{align*} \frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.11331, size = 2, normalized size = 0.4 \begin{align*} \frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10916, size = 19, normalized size = 3.8 \begin{align*} \frac{\arctan \left (\frac{{\left | a \right |} \tan \left (x\right )}{a}\right )}{{\left | a \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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