Optimal. Leaf size=8 \[ \frac {\sec ^6(x)}{6} \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, 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 30
Rule 2606
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*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 6, normalized size = 0.75 \[ \frac {1}{6 \, \cos \relax (x)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 6, normalized size = 0.75 \[ \frac {1}{6 \, \cos \relax (x)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.88 \[ \frac {\left (\sec ^{6}\relax (x )\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 10, normalized size = 1.25 \[ -\frac {1}{6 \, {\left (\sin \relax (x)^{2} - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 18, normalized size = 2.25 \[ \frac {{\mathrm {tan}\relax (x)}^2\,\left ({\mathrm {tan}\relax (x)}^4+3\,{\mathrm {tan}\relax (x)}^2+3\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 7, normalized size = 0.88 \[ \frac {1}{6 \cos ^{6}{\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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