Optimal. Leaf size=23 \[ \frac {5-2 x}{9 \sqrt {-x^2-4 x+5}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, 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 = {636} \[ \frac {5-2 x}{9 \sqrt {-x^2-4 x+5}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 636
Rubi steps
\begin {align*} \int \frac {x}{\left (5-4 x-x^2\right )^{3/2}} \, dx &=\frac {5-2 x}{9 \sqrt {5-4 x-x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 23, normalized size = 1.00 \[ \frac {5-2 x}{9 \sqrt {-x^2-4 x+5}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.86, size = 29, normalized size = 1.26 \[ \frac {\sqrt {-x^{2} - 4 \, x + 5} {\left (2 \, x - 5\right )}}{9 \, {\left (x^{2} + 4 \, x - 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.61, size = 29, normalized size = 1.26 \[ \frac {\sqrt {-x^{2} - 4 \, x + 5} {\left (2 \, x - 5\right )}}{9 \, {\left (x^{2} + 4 \, x - 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 26, normalized size = 1.13 \[ \frac {\left (x +5\right ) \left (x -1\right ) \left (2 x -5\right )}{9 \left (-x^{2}-4 x +5\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 30, normalized size = 1.30 \[ -\frac {2 \, x}{9 \, \sqrt {-x^{2} - 4 \, x + 5}} + \frac {5}{9 \, \sqrt {-x^{2} - 4 \, x + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 19, normalized size = 0.83 \[ -\frac {2\,x-5}{9\,\sqrt {-x^2-4\,x+5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x}{\left (- \left (x - 1\right ) \left (x + 5\right )\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________