Optimal. Leaf size=32 \[ -\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0284919, 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 \[ -\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.21249, size = 26, normalized size = 0.81 \[ - \frac{2 \log{\left (- 2 x + 1 \right )}}{121} + \frac{2 \log{\left (5 x + 3 \right )}}{121} - \frac{1}{11 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0160945, size = 30, normalized size = 0.94 \[ \frac{1}{121} \left (-\frac{11}{5 x+3}-2 \log (5-10 x)+2 \log (5 x+3)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 27, normalized size = 0.8 \[ -{\frac{1}{33+55\,x}}+{\frac{2\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{2\,\ln \left ( -1+2\,x \right ) }{121}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33029, size = 35, normalized size = 1.09 \[ -\frac{1}{11 \,{\left (5 \, x + 3\right )}} + \frac{2}{121} \, \log \left (5 \, x + 3\right ) - \frac{2}{121} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(2*x - 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214964, size = 50, normalized size = 1.56 \[ \frac{2 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 11}{121 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(2*x - 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.262757, size = 26, normalized size = 0.81 \[ - \frac{2 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{2 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{55 x + 33} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.206186, size = 34, normalized size = 1.06 \[ -\frac{1}{11 \,{\left (5 \, x + 3\right )}} - \frac{2}{121} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(2*x - 1)),x, algorithm="giac")
[Out]