Optimal. Leaf size=32 \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0291063, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^2*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.23839, size = 26, normalized size = 0.81 \[ - \frac{5 \log{\left (- 2 x + 1 \right )}}{121} + \frac{5 \log{\left (5 x + 3 \right )}}{121} + \frac{1}{11 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**2/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0154968, size = 38, normalized size = 1.19 \[ \frac{(5-10 x) \log (1-2 x)+5 (2 x-1) \log (10 x+6)-11}{121 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^2*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 27, normalized size = 0.8 \[{\frac{5\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{1}{-11+22\,x}}-{\frac{5\,\ln \left ( -1+2\,x \right ) }{121}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^2/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.32244, size = 35, normalized size = 1.09 \[ -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \, \log \left (5 \, x + 3\right ) - \frac{5}{121} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*(2*x - 1)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218131, size = 50, normalized size = 1.56 \[ \frac{5 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 5 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{121 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*(2*x - 1)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.262597, size = 26, normalized size = 0.81 \[ - \frac{5 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{22 x - 11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**2/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212463, size = 34, normalized size = 1.06 \[ -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)*(2*x - 1)^2),x, algorithm="giac")
[Out]