Optimal. Leaf size=5 \[ \cos (x)+\sec (x) \]
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Rubi [A] time = 0.02, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2590, 14} \[ \cos (x)+\sec (x) \]
Antiderivative was successfully verified.
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Rule 14
Rule 2590
Rubi steps
\begin {align*} \int \sin (x) \tan ^2(x) \, dx &=-\operatorname {Subst}\left (\int \frac {1-x^2}{x^2} \, dx,x,\cos (x)\right )\\ &=-\operatorname {Subst}\left (\int \left (-1+\frac {1}{x^2}\right ) \, dx,x,\cos (x)\right )\\ &=\cos (x)+\sec (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 5, normalized size = 1.00 \[ \cos (x)+\sec (x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 11, normalized size = 2.20 \[ \frac {\cos \relax (x)^{2} + 1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 7, normalized size = 1.40 \[ \frac {1}{\cos \relax (x)} + \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 20, normalized size = 4.00 \[ \frac {\sin ^{4}\relax (x )}{\cos \relax (x )}+\left (2+\sin ^{2}\relax (x )\right ) \cos \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 7, normalized size = 1.40 \[ \frac {1}{\cos \relax (x)} + \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.00, size = 7, normalized size = 1.40 \[ \cos \relax (x)+\frac {1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 7, normalized size = 1.40 \[ \cos {\relax (x )} + \frac {1}{\cos {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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