Optimal. Leaf size=23 \[ -\frac {1}{6} (2-3 x) \sqrt {4-12 x+9 x^2} \]
[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 = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {623}
\begin {gather*} -\frac {1}{6} (2-3 x) \sqrt {9 x^2-12 x+4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 623
Rubi steps
\begin {align*} \int \sqrt {4-12 x+9 x^2} \, dx &=-\frac {1}{6} (2-3 x) \sqrt {4-12 x+9 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 25, normalized size = 1.09 \begin {gather*} \frac {\sqrt {(2-3 x)^2} x (-4+3 x)}{-4+6 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
2.
time = 0.07, size = 16, normalized size = 0.70
method | result | size |
default | \(\frac {\mathrm {csgn}\left (-2+3 x \right ) \left (-2+3 x \right )^{2}}{6}\) | \(16\) |
gosper | \(\frac {x \left (3 x -4\right ) \sqrt {\left (-2+3 x \right )^{2}}}{-4+6 x}\) | \(25\) |
risch | \(\frac {3 \sqrt {\left (-2+3 x \right )^{2}}\, x^{2}}{2 \left (-2+3 x \right )}-\frac {2 \sqrt {\left (-2+3 x \right )^{2}}\, x}{-2+3 x}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.51, size = 30, normalized size = 1.30 \begin {gather*} \frac {1}{2} \, \sqrt {9 \, x^{2} - 12 \, x + 4} x - \frac {1}{3} \, \sqrt {9 \, x^{2} - 12 \, x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.38, size = 9, normalized size = 0.39 \begin {gather*} \frac {3}{2} \, x^{2} - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 8, normalized size = 0.35 \begin {gather*} \frac {3 x^{2}}{2} - 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.34, size = 26, normalized size = 1.13 \begin {gather*} \frac {1}{2} \, {\left (3 \, x^{2} - 4 \, x\right )} \mathrm {sgn}\left (3 \, x - 2\right ) + \frac {2}{3} \, \mathrm {sgn}\left (3 \, x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.11, size = 13, normalized size = 0.57 \begin {gather*} \frac {\left |3\,x-2\right |\,\left (3\,x-2\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________