Optimal. Leaf size=11 \[ -\frac{1}{\left (\sqrt{x}+1\right )^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0022699, antiderivative size = 11, normalized size of antiderivative = 1., 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.
[In]
[Out]
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*}
Mathematica [A] time = 0.0018168, size = 11, normalized size = 1. \[ -\frac{1}{\left (\sqrt{x}+1\right )^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 10, normalized size = 0.9 \begin{align*} - \left ( \sqrt{x}+1 \right ) ^{-2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.976081, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{{\left (\sqrt{x} + 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.30151, size = 51, normalized size = 4.64 \begin{align*} -\frac{x - 2 \, \sqrt{x} + 1}{x^{2} - 2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.438852, size = 12, normalized size = 1.09 \begin{align*} - \frac{1}{2 \sqrt{x} + x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10769, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{{\left (\sqrt{x} + 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]