Optimal. Leaf size=43 \[ \sqrt{2} 7^n \sqrt{x+1} F_1\left (\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4 (x+1)}{7},\frac{x+1}{2}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0781571, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \sqrt{2} 7^n \sqrt{x+1} F_1\left (\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4 (x+1)}{7},\frac{x+1}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[(3 - 4*x)^n/Sqrt[1 - x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.4871, size = 36, normalized size = 0.84 \[ \sqrt{2} \cdot 7^{n} \sqrt{x + 1} \operatorname{appellf_{1}}{\left (\frac{1}{2},\frac{1}{2},- n,\frac{3}{2},\frac{x}{2} + \frac{1}{2},\frac{4 x}{7} + \frac{4}{7} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3-4*x)**n/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0613273, size = 48, normalized size = 1.12 \[ -\frac{(3-4 x)^{n+1} F_1\left (n+1;\frac{1}{2},\frac{1}{2};n+2;\frac{1}{7} (3-4 x),4 x-3\right )}{\sqrt{7} (n+1)} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(3 - 4*x)^n/Sqrt[1 - x^2],x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.059, size = 0, normalized size = 0. \[ \int{ \left ( 3-4\,x \right ) ^{n}{\frac{1}{\sqrt{-{x}^{2}+1}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3-4*x)^n/(-x^2+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-4 \, x + 3\right )}^{n}}{\sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x + 3)^n/sqrt(-x^2 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (-4 \, x + 3\right )}^{n}}{\sqrt{-x^{2} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x + 3)^n/sqrt(-x^2 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (- 4 x + 3\right )^{n}}{\sqrt{- \left (x - 1\right ) \left (x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3-4*x)**n/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-4 \, x + 3\right )}^{n}}{\sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-4*x + 3)^n/sqrt(-x^2 + 1),x, algorithm="giac")
[Out]