Optimal. Leaf size=9 \[ -2 \log \left (\cos \left (\sqrt {x}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 3475
Rule 3747
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*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ -2 \log \left (\cos \left (\sqrt {x}\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 2.00, size = 13, normalized size = 1.44 \[ -\log \left (\frac {1}{\tan \left (\sqrt {x}\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 8, normalized size = 0.89 \[ -2 \, \log \left ({\left | \cos \left (\sqrt {x}\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 0.89 \[ -2 \ln \left (\cos \left (\sqrt {x}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 7, normalized size = 0.78 \[ 2 \, \log \left (\sec \left (\sqrt {x}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.18, size = 19, normalized size = 2.11 \[ -2\,\ln \left ({\mathrm {e}}^{\sqrt {x}\,2{}\mathrm {i}}+1\right )+\sqrt {x}\,2{}\mathrm {i} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 10, normalized size = 1.11 \[ \log {\left (\tan ^{2}{\left (\sqrt {x} \right )} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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