Optimal. Leaf size=31 \[ \frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0580792, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.029 \[ \frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)} \]
Antiderivative was successfully verified.
[In] Int[-3/(4 + 5*x)^2 - (5 + 4*x)/((4 + 5*x)^2*Sqrt[1 - x^2]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.61917, size = 19, normalized size = 0.61 \[ \frac{\sqrt{- x^{2} + 1}}{5 x + 4} + \frac{3}{5 \left (5 x + 4\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(-3/(4+5*x)**2+(-5-4*x)/(4+5*x)**2/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0532263, size = 23, normalized size = 0.74 \[ \frac{5 \sqrt{1-x^2}+3}{25 x+20} \]
Antiderivative was successfully verified.
[In] Integrate[-3/(4 + 5*x)^2 - (5 + 4*x)/((4 + 5*x)^2*Sqrt[1 - x^2]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.013, size = 32, normalized size = 1. \[{\frac{1}{5}\sqrt{- \left ( x+{\frac{4}{5}} \right ) ^{2}+{\frac{8\,x}{5}}+{\frac{41}{25}}} \left ( x+{\frac{4}{5}} \right ) ^{-1}}+{\frac{3}{20+25\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(-3/(4+5*x)^2+(-5-4*x)/(4+5*x)^2/(-x^2+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.04935, size = 36, normalized size = 1.16 \[ \frac{\sqrt{-x^{2} + 1}}{5 \, x + 4} + \frac{3}{5 \,{\left (5 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(4*x + 5)/(sqrt(-x^2 + 1)*(5*x + 4)^2) - 3/(5*x + 4)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.266149, size = 68, normalized size = 2.19 \[ -\frac{20 \, x^{2} - \sqrt{-x^{2} + 1}{\left (25 \, x + 12\right )} + 25 \, x + 12}{20 \,{\left (\sqrt{-x^{2} + 1}{\left (5 \, x + 4\right )} - 5 \, x - 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(4*x + 5)/(sqrt(-x^2 + 1)*(5*x + 4)^2) - 3/(5*x + 4)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \frac{4 x}{25 x^{2} \sqrt{- x^{2} + 1} + 40 x \sqrt{- x^{2} + 1} + 16 \sqrt{- x^{2} + 1}}\, dx - \int \frac{3 \sqrt{- x^{2} + 1}}{25 x^{2} \sqrt{- x^{2} + 1} + 40 x \sqrt{- x^{2} + 1} + 16 \sqrt{- x^{2} + 1}}\, dx - \int \frac{5}{25 x^{2} \sqrt{- x^{2} + 1} + 40 x \sqrt{- x^{2} + 1} + 16 \sqrt{- x^{2} + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-3/(4+5*x)**2+(-5-4*x)/(4+5*x)**2/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int -\frac{4 \, x + 5}{\sqrt{-x^{2} + 1}{\left (5 \, x + 4\right )}^{2}} - \frac{3}{{\left (5 \, x + 4\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(4*x + 5)/(sqrt(-x^2 + 1)*(5*x + 4)^2) - 3/(5*x + 4)^2,x, algorithm="giac")
[Out]