Optimal. Leaf size=22 \[ -\frac {2 (3-8 x)}{9 \sqrt {3 x-4 x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {627}
\begin {gather*} -\frac {2 (3-8 x)}{9 \sqrt {3 x-4 x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 627
Rubi steps
\begin {align*} \int \frac {1}{\left (3 x-4 x^2\right )^{3/2}} \, dx &=-\frac {2 (3-8 x)}{9 \sqrt {3 x-4 x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 21, normalized size = 0.95 \begin {gather*} \frac {2 (-3+8 x)}{9 \sqrt {-x (-3+4 x)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.38, size = 19, normalized size = 0.86
method | result | size |
default | \(-\frac {2 \left (3-8 x \right )}{9 \sqrt {-4 x^{2}+3 x}}\) | \(19\) |
meijerg | \(-\frac {2 \sqrt {3}\, \left (1-\frac {8 x}{3}\right )}{9 \sqrt {x}\, \sqrt {-\frac {4 x}{3}+1}}\) | \(21\) |
gosper | \(-\frac {2 x \left (-3+4 x \right ) \left (-3+8 x \right )}{9 \left (-4 x^{2}+3 x \right )^{\frac {3}{2}}}\) | \(25\) |
trager | \(-\frac {2 \left (-3+8 x \right ) \sqrt {-4 x^{2}+3 x}}{9 x \left (-3+4 x \right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 28, normalized size = 1.27 \begin {gather*} \frac {16 \, x}{9 \, \sqrt {-4 \, x^{2} + 3 \, x}} - \frac {2}{3 \, \sqrt {-4 \, x^{2} + 3 \, x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.65, size = 29, normalized size = 1.32 \begin {gather*} -\frac {2 \, \sqrt {-4 \, x^{2} + 3 \, x} {\left (8 \, x - 3\right )}}{9 \, {\left (4 \, x^{2} - 3 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (- 4 x^{2} + 3 x\right )^{\frac {3}{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.67, size = 29, normalized size = 1.32 \begin {gather*} -\frac {2 \, \sqrt {-4 \, x^{2} + 3 \, x} {\left (8 \, x - 3\right )}}{9 \, {\left (4 \, x^{2} - 3 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.14, size = 18, normalized size = 0.82 \begin {gather*} \frac {16\,x-6}{9\,\sqrt {3\,x-4\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________