Optimal. Leaf size=15 \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0023161, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {261} \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{\sqrt{1+\sqrt{x}}}{\sqrt{x}} \, dx &=\frac{4}{3} \left (1+\sqrt{x}\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0022676, size = 15, normalized size = 1. \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 10, normalized size = 0.7 \begin{align*}{\frac{4}{3} \left ( \sqrt{x}+1 \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.970264, size = 12, normalized size = 0.8 \begin{align*} \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.22614, size = 34, normalized size = 2.27 \begin{align*} \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.283027, size = 31, normalized size = 2.07 \begin{align*} \frac{4 \sqrt{x} \sqrt{\sqrt{x} + 1}}{3} + \frac{4 \sqrt{\sqrt{x} + 1}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11483, size = 12, normalized size = 0.8 \begin{align*} \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]