Optimal. Leaf size=16 \[ 2 \tan \left (\sqrt {x}\right )-2 \sqrt {x} \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, 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 8
Rule 3473
Rule 3747
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*}
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Mathematica [A] time = 0.04, 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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fricas [A] time = 1.97, size = 12, normalized size = 0.75 \[ -2 \, \sqrt {x} + 2 \, \tan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 12, normalized size = 0.75 \[ -2 \, \sqrt {x} + 2 \, \tan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.81 \[ -2 \sqrt {x}+2 \tan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 12, normalized size = 0.75 \[ -2 \, \sqrt {x} + 2 \, \tan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.58, size = 20, normalized size = 1.25 \[ -2\,\sqrt {x}+\frac {4{}\mathrm {i}}{{\mathrm {e}}^{\sqrt {x}\,2{}\mathrm {i}}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 14, normalized size = 0.88 \[ - 2 \sqrt {x} + 2 \tan {\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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