Optimal. Leaf size=18 \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014717, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {74} \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 74
Rubi steps
\begin{align*} \int \sqrt{-1+x} x \sqrt{1+x} \, dx &=\frac{1}{3} (-1+x)^{3/2} (1+x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0037917, size = 18, normalized size = 1. \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.7 \begin{align*}{\frac{1}{3} \left ( -1+x \right ) ^{{\frac{3}{2}}} \left ( 1+x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.17424, size = 12, normalized size = 0.67 \begin{align*} \frac{1}{3} \,{\left (x^{2} - 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.55008, size = 53, normalized size = 2.94 \begin{align*} \frac{1}{3} \,{\left (x^{2} - 1\right )} \sqrt{x + 1} \sqrt{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int x \sqrt{x - 1} \sqrt{x + 1}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.85908, size = 16, normalized size = 0.89 \begin{align*} \frac{1}{3} \,{\left (x + 1\right )}^{\frac{3}{2}}{\left (x - 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]