Optimal. Leaf size=11 \[ \frac {\sin (x)}{a \cos (x)+a} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2648} \[ \frac {\sin (x)}{a \cos (x)+a} \]
Antiderivative was successfully verified.
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Rule 2648
Rubi steps
\begin {align*} \int \frac {1}{a+a \cos (x)} \, dx &=\frac {\sin (x)}{a+a \cos (x)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.91 \[ \frac {\tan \left (\frac {x}{2}\right )}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 11, normalized size = 1.00 \[ \frac {\sin \relax (x)}{a \cos \relax (x) + a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 8, normalized size = 0.73 \[ \frac {\tan \left (\frac {1}{2} \, x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 0.82 \[ \frac {\tan \left (\frac {x}{2}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 12, normalized size = 1.09 \[ \frac {\sin \relax (x)}{a {\left (\cos \relax (x) + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.29, size = 8, normalized size = 0.73 \[ \frac {\mathrm {tan}\left (\frac {x}{2}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 5, normalized size = 0.45 \[ \frac {\tan {\left (\frac {x}{2} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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