Optimal. Leaf size=5 \[ \frac {x}{a^2} \]
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Rubi [A] time = 0.04, antiderivative size = 5, 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, 8} \[ \frac {x}{a^2} \]
Antiderivative was successfully verified.
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Rule 8
Rule 3175
Rubi steps
\begin {align*} \int \frac {\cos ^4(x)}{\left (a-a \sin ^2(x)\right )^2} \, dx &=\frac {\int 1 \, dx}{a^2}\\ &=\frac {x}{a^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 5, normalized size = 1.00 \[ \frac {x}{a^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 5, normalized size = 1.00 \[ \frac {x}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 5, normalized size = 1.00 \[ \frac {x}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.19, size = 8, normalized size = 1.60 \[ \frac {\arctan \left (\tan \relax (x )\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 5, normalized size = 1.00 \[ \frac {x}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 13.94, size = 5, normalized size = 1.00 \[ \frac {x}{a^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.00, size = 3, normalized size = 0.60 \[ \frac {x}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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