Optimal. Leaf size=18 \[ F\left (\sin ^{-1}\left (\frac {\sqrt {1+x}}{\sqrt {3}}\right )|\frac {3}{4}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {120}
\begin {gather*} F\left (\text {ArcSin}\left (\frac {\sqrt {x+1}}{\sqrt {3}}\right )|\frac {3}{4}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 120
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {2-x} \sqrt {3-x} \sqrt {1+x}} \, dx &=F\left (\sin ^{-1}\left (\frac {\sqrt {1+x}}{\sqrt {3}}\right )|\frac {3}{4}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] Result contains complex when optimal does not.
time = 1.28, size = 65, normalized size = 3.61 \begin {gather*} -\frac {2 i \sqrt {1-\frac {3}{2-x}} \sqrt {1+\frac {1}{2-x}} (2-x) F\left (\left .i \sinh ^{-1}\left (\frac {1}{\sqrt {2-x}}\right )\right |-3\right )}{\sqrt {-((-3+x) (1+x))}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.15, size = 19, normalized size = 1.06
method | result | size |
default | \(\frac {2 \sqrt {3}\, \EllipticF \left (\frac {\sqrt {1+x}}{2}, \frac {2 \sqrt {3}}{3}\right )}{3}\) | \(19\) |
elliptic | \(\frac {2 \sqrt {\left (-2+x \right ) \left (-3+x \right ) \left (1+x \right )}\, \sqrt {6-3 x}\, \EllipticF \left (\frac {\sqrt {1+x}}{2}, \frac {2 \sqrt {3}}{3}\right )}{3 \sqrt {2-x}\, \sqrt {x^{3}-4 x^{2}+x +6}}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [C] Result contains higher order function than in optimal. Order 9 vs. order
4.
time = 0.12, size = 8, normalized size = 0.44 \begin {gather*} 2 \, {\rm weierstrassPInverse}\left (\frac {52}{3}, -\frac {280}{27}, x - \frac {4}{3}\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}{\sqrt {2 - x} \sqrt {3 - x} \sqrt {x + 1}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {1}{\sqrt {x+1}\,\sqrt {2-x}\,\sqrt {3-x}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________