Optimal. Leaf size=21 \[ x+4 \sqrt{x}+4 \log \left (1-\sqrt{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0112809, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {376, 77} \[ x+4 \sqrt{x}+4 \log \left (1-\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 376
Rule 77
Rubi steps
\begin{align*} \int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \frac{x (1+x)}{-1+x} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (2+\frac{2}{-1+x}+x\right ) \, dx,x,\sqrt{x}\right )\\ &=4 \sqrt{x}+x+4 \log \left (1-\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0079634, size = 20, normalized size = 0.95 \[ x+4 \left (\sqrt{x}+\log \left (1-\sqrt{x}\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 16, normalized size = 0.8 \begin{align*} x+4\,\sqrt{x}+4\,\ln \left ( \sqrt{x}-1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.950811, size = 20, normalized size = 0.95 \begin{align*} x + 4 \, \sqrt{x} + 4 \, \log \left (\sqrt{x} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.19142, size = 49, normalized size = 2.33 \begin{align*} x + 4 \, \sqrt{x} + 4 \, \log \left (\sqrt{x} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.136053, size = 17, normalized size = 0.81 \begin{align*} 4 \sqrt{x} + x + 4 \log{\left (\sqrt{x} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05136, size = 22, normalized size = 1.05 \begin{align*} x + 4 \, \sqrt{x} + 4 \, \log \left ({\left | \sqrt{x} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]