Optimal. Leaf size=13 \[ \frac{1}{2} \left (\sqrt{x}+1\right )^4 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0022539, antiderivative size = 13, 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} \[ \frac{1}{2} \left (\sqrt{x}+1\right )^4 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{\left (1+\sqrt{x}\right )^3}{\sqrt{x}} \, dx &=\frac{1}{2} \left (1+\sqrt{x}\right )^4\\ \end{align*}
Mathematica [A] time = 0.0024674, size = 13, normalized size = 1. \[ \frac{1}{2} \left (\sqrt{x}+1\right )^4 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.001, size = 20, normalized size = 1.5 \begin{align*}{\frac{{x}^{2}}{2}}+2\,{x}^{3/2}+3\,x+2\,\sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.989979, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{2} \,{\left (\sqrt{x} + 1\right )}^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.23182, size = 47, normalized size = 3.62 \begin{align*} \frac{1}{2} \, x^{2} + 2 \,{\left (x + 1\right )} \sqrt{x} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.163897, size = 20, normalized size = 1.54 \begin{align*} 2 x^{\frac{3}{2}} + 2 \sqrt{x} + \frac{x^{2}}{2} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.09194, size = 26, normalized size = 2. \begin{align*} \frac{1}{2} \, x^{2} + 2 \, x^{\frac{3}{2}} + 3 \, x + 2 \, \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]