Optimal. Leaf size=12 \[ \frac{2}{3} (\log (x)+1)^{3/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0256897, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2302, 30} \[ \frac{2}{3} (\log (x)+1)^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\sqrt{1+\log (x)}}{x} \, dx &=\operatorname{Subst}\left (\int \sqrt{x} \, dx,x,1+\log (x)\right )\\ &=\frac{2}{3} (1+\log (x))^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0037376, size = 12, normalized size = 1. \[ \frac{2}{3} (\log (x)+1)^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 9, normalized size = 0.8 \begin{align*}{\frac{2}{3} \left ( 1+\ln \left ( x \right ) \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.11695, size = 11, normalized size = 0.92 \begin{align*} \frac{2}{3} \,{\left (\log \left (x\right ) + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.04066, size = 32, normalized size = 2.67 \begin{align*} \frac{2}{3} \,{\left (\log \left (x\right ) + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.738572, size = 10, normalized size = 0.83 \begin{align*} \frac{2 \left (\log{\left (x \right )} + 1\right )^{\frac{3}{2}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.29265, size = 11, normalized size = 0.92 \begin{align*} \frac{2}{3} \,{\left (\log \left (x\right ) + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]