Optimal. Leaf size=14 \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt {4-x}\right )\right |-1\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {703, 227}
\begin {gather*} -2 F\left (\left .\text {ArcSin}\left (\sqrt {4-x}\right )\right |-1\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 227
Rule 703
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {4-x} \sqrt {-15+8 x-x^2}} \, dx &=-\left (2 \text {Subst}\left (\int \frac {1}{\sqrt {1-x^4}} \, dx,x,\sqrt {4-x}\right )\right )\\ &=-2 F\left (\left .\sin ^{-1}\left (\sqrt {4-x}\right )\right |-1\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] Result contains higher order function than in optimal. Order 5 vs. order 4 in
optimal.
time = 10.02, size = 28, normalized size = 2.00 \begin {gather*} -2 \sqrt {4-x} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};(4-x)^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs.
\(2(12)=24\).
time = 0.13, size = 41, normalized size = 2.93
method | result | size |
default | \(\frac {\EllipticF \left (\frac {\sqrt {-6+2 x}}{2}, \sqrt {2}\right ) \sqrt {10-2 x}\, \sqrt {-6+2 x}}{\sqrt {-x^{2}+8 x -15}}\) | \(41\) |
elliptic | \(\frac {\sqrt {\left (-4+x \right ) \left (x^{2}-8 x +15\right )}\, \sqrt {-6+2 x}\, \sqrt {10-2 x}\, \EllipticF \left (\frac {\sqrt {-6+2 x}}{2}, \sqrt {2}\right )}{\sqrt {-x^{2}+8 x -15}\, \sqrt {x^{3}-12 x^{2}+47 x -60}}\) | \(70\) |
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 = 0.13, size = 8, normalized size = 0.57 \begin {gather*} 2 \, {\rm weierstrassPInverse}\left (4, 0, x - 4\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 {- \left (x - 5\right ) \left (x - 3\right )} \sqrt {4 - x}}\, 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 = -0.07 \begin {gather*} \int \frac {1}{\sqrt {4-x}\,\sqrt {-x^2+8\,x-15}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________