Optimal. Leaf size=8 \[ \frac{\sec ^6(x)}{6} \]
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Rubi [A] time = 0.0134191, 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} \[ \frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
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Rule 2606
Rule 30
Rubi steps
\begin{align*} \int \sec ^6(x) \tan (x) \, dx &=\operatorname{Subst}\left (\int x^5 \, dx,x,\sec (x)\right )\\ &=\frac{\sec ^6(x)}{6}\\ \end{align*}
Mathematica [A] time = 0.0040709, size = 8, normalized size = 1. \[ \frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 7, normalized size = 0.9 \begin{align*}{\frac{ \left ( \sec \left ( x \right ) \right ) ^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924682, size = 14, normalized size = 1.75 \begin{align*} -\frac{1}{6 \,{\left (\sin \left (x\right )^{2} - 1\right )}^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.00347, size = 19, normalized size = 2.38 \begin{align*} \frac{1}{6 \, \cos \left (x\right )^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067629, size = 7, normalized size = 0.88 \begin{align*} \frac{1}{6 \cos ^{6}{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05836, size = 8, normalized size = 1. \begin{align*} \frac{1}{6 \, \cos \left (x\right )^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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