Optimal. Leaf size=6 \[ \tan ^{-1}\left (\sqrt {x}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 6, 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 = {12, 63, 203} \[ \tan ^{-1}\left (\sqrt {x}\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 63
Rule 203
Rubi steps
\begin {align*} \int \frac {1}{2 \sqrt {x} (1+x)} \, dx &=\frac {1}{2} \int \frac {1}{\sqrt {x} (1+x)} \, dx\\ &=\operatorname {Subst}\left (\int \frac {1}{1+x^2} \, dx,x,\sqrt {x}\right )\\ &=\tan ^{-1}\left (\sqrt {x}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 1.00 \[ \tan ^{-1}\left (\sqrt {x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 4, normalized size = 0.67 \[ \arctan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 4, normalized size = 0.67 \[ \arctan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 5, normalized size = 0.83 \[ \arctan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.39, size = 4, normalized size = 0.67 \[ \arctan \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 4, normalized size = 0.67 \[ \mathrm {atan}\left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 5, normalized size = 0.83 \[ \operatorname {atan}{\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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