Optimal. Leaf size=8 \[ \tan ^{-1}\left (\sqrt {x}\right )^2 \]
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Rubi [A]
time = 0.02, 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 = {65, 209, 6818}
\begin {gather*} \tan ^{-1}\left (\sqrt {x}\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 65
Rule 209
Rule 6818
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 = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \tan ^{-1}\left (\sqrt {x}\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 1.78, size = 7, normalized size = 0.88 \begin {gather*} \text {ConditionalExpression}\left [\text {ArcTan}\left [\sqrt {x}\right ],\left \{\text {True}\right \}\right ] \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.06, size = 7, normalized size = 0.88
method | result | size |
derivativedivides | \(\arctan \left (\sqrt {x}\right )^{2}\) | \(7\) |
default | \(\arctan \left (\sqrt {x}\right )^{2}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 6, normalized size = 0.75 \begin {gather*} \arctan \left (\sqrt {x}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 6, normalized size = 0.75 \begin {gather*} \arctan \left (\sqrt {x}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.44, size = 7, normalized size = 0.88 \begin {gather*} \operatorname {atan}^{2}{\left (\sqrt {x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 12, normalized size = 1.50 \begin {gather*} \frac {2}{2} \arctan ^{2}\left (\sqrt {x}\right ) \end {gather*}
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 \begin {gather*} {\mathrm {atan}\left (\sqrt {x}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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