Optimal. Leaf size=11 \[ -\frac {2}{1+\sqrt {x}} \]
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Rubi [A]
time = 0.00, antiderivative size = 11, 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 = {267}
\begin {gather*} -\frac {2}{\sqrt {x}+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {1}{\left (1+\sqrt {x}\right )^2 \sqrt {x}} \, dx &=-\frac {2}{1+\sqrt {x}}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2}{1+\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 10, normalized size = 0.91
method | result | size |
derivativedivides | \(-\frac {2}{\sqrt {x}+1}\) | \(10\) |
default | \(-\frac {2}{\sqrt {x}+1}\) | \(10\) |
meijerg | \(\frac {2 \sqrt {x}}{\sqrt {x}+1}\) | \(13\) |
trager | \(-\frac {2 \left (x -2\right )}{x -1}-\frac {2 \sqrt {x}}{x -1}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 9, normalized size = 0.82 \begin {gather*} -\frac {2}{\sqrt {x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 12, normalized size = 1.09 \begin {gather*} -\frac {2 \, {\left (\sqrt {x} - 1\right )}}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 8, normalized size = 0.73 \begin {gather*} - \frac {2}{\sqrt {x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.67, size = 9, normalized size = 0.82 \begin {gather*} -\frac {2}{\sqrt {x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 9, normalized size = 0.82 \begin {gather*} -\frac {2}{\sqrt {x}+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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