Optimal. Leaf size=16 \[ 2 \tan \left (\sqrt{x}\right )-2 \sqrt{x} \]
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Rubi [A] time = 0.0178689, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214, Rules used = {3747, 3473, 8} \[ 2 \tan \left (\sqrt{x}\right )-2 \sqrt{x} \]
Antiderivative was successfully verified.
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Rule 3747
Rule 3473
Rule 8
Rubi steps
\begin{align*} \int \frac{\tan ^2\left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \tan ^2(x) \, dx,x,\sqrt{x}\right )\\ &=2 \tan \left (\sqrt{x}\right )-2 \operatorname{Subst}\left (\int 1 \, dx,x,\sqrt{x}\right )\\ &=-2 \sqrt{x}+2 \tan \left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.034028, size = 18, normalized size = 1.12 \[ 2 \tan \left (\sqrt{x}\right )-2 \tan ^{-1}\left (\tan \left (\sqrt{x}\right )\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 13, normalized size = 0.8 \begin{align*} -2\,\sqrt{x}+2\,\tan \left ( \sqrt{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.47961, size = 16, normalized size = 1. \begin{align*} -2 \, \sqrt{x} + 2 \, \tan \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.28983, size = 39, normalized size = 2.44 \begin{align*} -2 \, \sqrt{x} + 2 \, \tan \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.02012, size = 14, normalized size = 0.88 \begin{align*} - 2 \sqrt{x} + 2 \tan{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11438, size = 16, normalized size = 1. \begin{align*} -2 \, \sqrt{x} + 2 \, \tan \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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