Optimal. Leaf size=19 \[ -\frac {2}{\sqrt {x+1}}-\frac {2}{\sqrt {x-1}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.27, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6688} \[ -\frac {2}{\sqrt {x+1}}-\frac {2}{\sqrt {x-1}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6688
Rubi steps
\begin {align*} \int \frac {(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx &=\int \left (\frac {1}{(-1+x)^{3/2}}+\frac {1}{(1+x)^{3/2}}\right ) \, dx\\ &=-\frac {2}{\sqrt {-1+x}}-\frac {2}{\sqrt {1+x}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 19, normalized size = 1.00 \[ -\frac {2}{\sqrt {x+1}}-\frac {2}{\sqrt {x-1}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.99, size = 28, normalized size = 1.47 \[ -\frac {2 \, {\left ({\left (x + 1\right )} \sqrt {x - 1} + \sqrt {x + 1} {\left (x - 1\right )}\right )}}{x^{2} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.15, size = 15, normalized size = 0.79 \[ -\frac {2}{\sqrt {x + 1}} - \frac {2}{\sqrt {x - 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 16, normalized size = 0.84 \[ -\frac {2}{\sqrt {x -1}}-\frac {2}{\sqrt {x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.63, size = 15, normalized size = 0.79 \[ -\frac {2}{\sqrt {x + 1}} - \frac {2}{\sqrt {x - 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.40, size = 15, normalized size = 0.79 \[ -\frac {2}{\sqrt {x-1}}-\frac {2}{\sqrt {x+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 6.63, size = 56, normalized size = 2.95 \[ - \frac {2 x \sqrt {x - 1}}{x^{2} - 1} - \frac {2 x \sqrt {x + 1}}{x^{2} - 1} - \frac {2 \sqrt {x - 1}}{x^{2} - 1} + \frac {2 \sqrt {x + 1}}{x^{2} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________