Optimal. Leaf size=7 \[ -\log \left (\cos \left (e^x\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2282, 3475} \[ -\log \left (\cos \left (e^x\right )\right ) \]
Antiderivative was successfully verified.
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Rule 2282
Rule 3475
Rubi steps
\begin {align*} \int e^x \tan \left (e^x\right ) \, dx &=\operatorname {Subst}\left (\int \tan (x) \, dx,x,e^x\right )\\ &=-\log \left (\cos \left (e^x\right )\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 7, normalized size = 1.00 \[ -\log \left (\cos \left (e^x\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.10, size = 12, normalized size = 1.71 \[ -\frac {1}{2} \, \log \left (\frac {1}{\tan \left (e^{x}\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 7, normalized size = 1.00 \[ -\log \left ({\left | \cos \left (e^{x}\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 1.00 \[ -\ln \left (\cos \left ({\mathrm e}^{x}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 4, normalized size = 0.57 \[ \log \left (\sec \left (e^{x}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.65, size = 10, normalized size = 1.43 \[ \frac {\ln \left ({\mathrm {tan}\left ({\mathrm {e}}^x\right )}^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 10, normalized size = 1.43 \[ \frac {\log {\left (\tan ^{2}{\left (e^{x} \right )} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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