Optimal. Leaf size=10 \[ 2 \log \left (1+\sqrt {x}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {266}
\begin {gather*} 2 \log \left (\sqrt {x}+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 266
Rubi steps
\begin {align*} \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx &=2 \log \left (1+\sqrt {x}\right )\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 10, normalized size = 1.00 \begin {gather*} 2 \log \left (1+\sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 9, normalized size = 0.90
method | result | size |
derivativedivides | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
default | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
meijerg | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
trager | \(\ln \left (x +2 \sqrt {x}+1\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 8, normalized size = 0.80 \begin {gather*} 2 \, \log \left (\sqrt {x} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 8, normalized size = 0.80 \begin {gather*} 2 \, \log \left (\sqrt {x} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} 2 \log {\left (\sqrt {x} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.04, size = 8, normalized size = 0.80 \begin {gather*} 2 \, \log \left (\sqrt {x} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} 2\,\ln \left (\sqrt {x}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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