Optimal. Leaf size=53 \[ \frac{125}{24} (1-2 x)^{3/2}-\frac{825}{8} \sqrt{1-2 x}-\frac{1815}{8 \sqrt{1-2 x}}+\frac{1331}{24 (1-2 x)^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0360355, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{125}{24} (1-2 x)^{3/2}-\frac{825}{8} \sqrt{1-2 x}-\frac{1815}{8 \sqrt{1-2 x}}+\frac{1331}{24 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/(1 - 2*x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.11743, size = 46, normalized size = 0.87 \[ \frac{125 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{825 \sqrt{- 2 x + 1}}{8} - \frac{1815}{8 \sqrt{- 2 x + 1}} + \frac{1331}{24 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0307891, size = 28, normalized size = 0.53 \[ -\frac{125 x^3+1050 x^2-2505 x+808}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/(1 - 2*x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 25, normalized size = 0.5 \[ -{\frac{125\,{x}^{3}+1050\,{x}^{2}-2505\,x+808}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34315, size = 45, normalized size = 0.85 \[ \frac{125}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{825}{8} \, \sqrt{-2 \, x + 1} + \frac{121 \,{\left (45 \, x - 17\right )}}{12 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211852, size = 42, normalized size = 0.79 \[ \frac{125 \, x^{3} + 1050 \, x^{2} - 2505 \, x + 808}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.151, size = 102, normalized size = 1.92 \[ \frac{125 x^{3}}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} + \frac{1050 x^{2}}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} - \frac{2505 x}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} + \frac{808}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212442, size = 54, normalized size = 1.02 \[ \frac{125}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{825}{8} \, \sqrt{-2 \, x + 1} - \frac{121 \,{\left (45 \, x - 17\right )}}{12 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]