Optimal. Leaf size=9 \[ -2 \log \left (\cos \left (\sqrt{x}\right )\right ) \]
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Rubi [A] time = 0.0097141, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {3747, 3475} \[ -2 \log \left (\cos \left (\sqrt{x}\right )\right ) \]
Antiderivative was successfully verified.
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Rule 3747
Rule 3475
Rubi steps
\begin{align*} \int \frac{\tan \left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \tan (x) \, dx,x,\sqrt{x}\right )\\ &=-2 \log \left (\cos \left (\sqrt{x}\right )\right )\\ \end{align*}
Mathematica [A] time = 0.0120247, size = 9, normalized size = 1. \[ -2 \log \left (\cos \left (\sqrt{x}\right )\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 8, normalized size = 0.9 \begin{align*} -2\,\ln \left ( \cos \left ( \sqrt{x} \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01361, size = 9, normalized size = 1. \begin{align*} 2 \, \log \left (\sec \left (\sqrt{x}\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.3592, size = 41, normalized size = 4.56 \begin{align*} -\log \left (\frac{1}{\tan \left (\sqrt{x}\right )^{2} + 1}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.991418, size = 10, normalized size = 1.11 \begin{align*} \log{\left (\tan ^{2}{\left (\sqrt{x} \right )} + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10323, size = 11, normalized size = 1.22 \begin{align*} -2 \, \log \left ({\left | \cos \left (\sqrt{x}\right ) \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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