Optimal. Leaf size=8 \[ \frac{\sec ^2(x)}{2} \]
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Rubi [A] time = 0.0106558, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {2606, 30} \[ \frac{\sec ^2(x)}{2} \]
Antiderivative was successfully verified.
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Rule 2606
Rule 30
Rubi steps
\begin{align*} \int \sec ^2(x) \tan (x) \, dx &=\operatorname{Subst}(\int x \, dx,x,\sec (x))\\ &=\frac{\sec ^2(x)}{2}\\ \end{align*}
Mathematica [A] time = 0.0041911, size = 8, normalized size = 1. \[ \frac{\sec ^2(x)}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 7, normalized size = 0.9 \begin{align*}{\frac{ \left ( \sec \left ( x \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.935947, size = 8, normalized size = 1. \begin{align*} \frac{1}{2} \, \tan \left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59947, size = 19, normalized size = 2.38 \begin{align*} \frac{1}{2 \, \cos \left (x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066424, size = 7, normalized size = 0.88 \begin{align*} \frac{1}{2 \cos ^{2}{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06617, size = 8, normalized size = 1. \begin{align*} \frac{1}{2 \, \cos \left (x\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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