Optimal. Leaf size=8 \[ \tan ^{-1}\left (\sqrt {x}\right )^2 \]
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Rubi [A] time = 0.03, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {63, 203, 6686} \[ \tan ^{-1}\left (\sqrt {x}\right )^2 \]
Antiderivative was successfully verified.
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Rule 63
Rule 203
Rule 6686
Rubi steps
\begin {align*} \int \frac {\tan ^{-1}\left (\sqrt {x}\right )}{\sqrt {x} (1+x)} \, dx &=\tan ^{-1}\left (\sqrt {x}\right )^2\\ \end {align*}
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Mathematica [A] time = 0.01, size = 8, normalized size = 1.00 \[ \tan ^{-1}\left (\sqrt {x}\right )^2 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 6, normalized size = 0.75 \[ \arctan \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 6, normalized size = 0.75 \[ \arctan \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 0.88 \[ \arctan \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 6, normalized size = 0.75 \[ \arctan \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.66, size = 6, normalized size = 0.75 \[ {\mathrm {atan}\left (\sqrt {x}\right )}^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.40, size = 7, normalized size = 0.88 \[ \operatorname {atan}^{2}{\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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