Optimal. Leaf size=40 \[ -\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0297779, antiderivative size = 40, 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 \[ -\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/(1 - 2*x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.1189, size = 34, normalized size = 0.85 \[ - \frac{25 \sqrt{- 2 x + 1}}{4} - \frac{55}{2 \sqrt{- 2 x + 1}} + \frac{121}{12 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0285201, size = 23, normalized size = 0.57 \[ \frac{-75 x^2+240 x-71}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/(1 - 2*x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 20, normalized size = 0.5 \[ -{\frac{75\,{x}^{2}-240\,x+71}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33272, size = 32, normalized size = 0.8 \[ -\frac{25}{4} \, \sqrt{-2 \, x + 1} + \frac{11 \,{\left (60 \, x - 19\right )}}{12 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21317, size = 35, normalized size = 0.88 \[ \frac{75 \, x^{2} - 240 \, x + 71}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.11617, size = 75, normalized size = 1.88 \[ \frac{75 x^{2}}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} - \frac{240 x}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} + \frac{71}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209473, size = 42, normalized size = 1.05 \[ -\frac{25}{4} \, \sqrt{-2 \, x + 1} - \frac{11 \,{\left (60 \, x - 19\right )}}{12 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]