Optimal. Leaf size=11 \[ -\frac {1}{\left (\sqrt {x}+1\right )^2} \]
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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 = {261} \[ -\frac {1}{\left (\sqrt {x}+1\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {1}{\left (1+\sqrt {x}\right )^3 \sqrt {x}} \, dx &=-\frac {1}{\left (1+\sqrt {x}\right )^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ -\frac {1}{\left (\sqrt {x}+1\right )^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.86, size = 20, normalized size = 1.82 \[ -\frac {x - 2 \, \sqrt {x} + 1}{x^{2} - 2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.82 \[ -\frac {1}{{\left (\sqrt {x} + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.91 \[ -\frac {1}{\left (\sqrt {x}+1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 9, normalized size = 0.82 \[ -\frac {1}{{\left (\sqrt {x} + 1\right )}^{2}} \]
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 \[ -\frac {1}{{\left (\sqrt {x}+1\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 12, normalized size = 1.09 \[ - \frac {1}{2 \sqrt {x} + x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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