Optimal. Leaf size=21 \[ \frac {x}{9 \sqrt {3-x} \sqrt {3+x}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {39}
\begin {gather*} \frac {x}{9 \sqrt {3-x} \sqrt {x+3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 39
Rubi steps
\begin {align*} \int \frac {1}{(3-x)^{3/2} (3+x)^{3/2}} \, dx &=\frac {x}{9 \sqrt {3-x} \sqrt {3+x}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 16, normalized size = 0.76 \begin {gather*} \frac {x}{9 \sqrt {9-x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 2 in
optimal.
time = 3.00, size = 66, normalized size = 3.14 \begin {gather*} \text {Piecewise}\left [\left \{\left \{-\frac {x \sqrt {\frac {3-x}{3+x}}}{-27+9 x},\frac {1}{\text {Abs}\left [3+x\right ]}>\frac {1}{6}\right \}\right \},-\frac {I}{9 \sqrt {1-\frac {6}{3+x}}}+\frac {I}{3 \sqrt {1-\frac {6}{3+x}} \left (3+x\right )}\right ] \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.16, size = 30, normalized size = 1.43
method | result | size |
gosper | \(\frac {x}{9 \sqrt {3-x}\, \sqrt {3+x}}\) | \(16\) |
default | \(\frac {1}{3 \sqrt {3-x}\, \sqrt {3+x}}-\frac {\sqrt {3-x}}{9 \sqrt {3+x}}\) | \(30\) |
risch | \(\frac {\sqrt {\left (3+x \right ) \left (3-x \right )}\, x}{9 \sqrt {3-x}\, \sqrt {3+x}\, \sqrt {-\left (-3+x \right ) \left (3+x \right )}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 12, normalized size = 0.57 \begin {gather*} \frac {x}{9 \, \sqrt {-x^{2} + 9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.29, size = 22, normalized size = 1.05 \begin {gather*} -\frac {\sqrt {x + 3} x \sqrt {-x + 3}}{9 \, {\left (x^{2} - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [C] Result contains complex when optimal does not.
time = 0.99, size = 71, normalized size = 3.38 \begin {gather*} \begin {cases} - \frac {\sqrt {-1 + \frac {6}{x + 3}} \left (x + 3\right )}{9 x - 27} + \frac {3 \sqrt {-1 + \frac {6}{x + 3}}}{9 x - 27} & \text {for}\: \frac {1}{\left |{x + 3}\right |} > \frac {1}{6} \\- \frac {i}{9 \sqrt {1 - \frac {6}{x + 3}}} + \frac {i}{3 \sqrt {1 - \frac {6}{x + 3}} \left (x + 3\right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 57 vs.
\(2 (15) = 30\).
time = 0.00, size = 87, normalized size = 4.14 \begin {gather*} 2 \left (\frac {\sqrt {-x+3}}{36 \left (2 \sqrt {6}-2 \sqrt {x+3}\right )}-\frac {2 \sqrt {6}-2 \sqrt {x+3}}{144 \sqrt {-x+3}}-\frac {\sqrt {-x+3} \sqrt {x+3}}{36 \left (x+3\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.36, size = 22, normalized size = 1.05 \begin {gather*} -\frac {x\,\sqrt {3-x}}{\left (9\,x-27\right )\,\sqrt {x+3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________