Optimal. Leaf size=31 \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0451922, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.4793, size = 29, normalized size = 0.94 \[ - \frac{2 \log{\left (- 2 x + 1 \right )}}{77} - \frac{3 \log{\left (3 x + 2 \right )}}{7} + \frac{5 \log{\left (5 x + 3 \right )}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0115671, size = 31, normalized size = 1. \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 26, normalized size = 0.8 \[{\frac{5\,\ln \left ( 3+5\,x \right ) }{11}}-{\frac{3\,\ln \left ( 2+3\,x \right ) }{7}}-{\frac{2\,\ln \left ( -1+2\,x \right ) }{77}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33952, size = 34, normalized size = 1.1 \[ \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)*(2*x - 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216573, size = 34, normalized size = 1.1 \[ \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)*(2*x - 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.308153, size = 29, normalized size = 0.94 \[ - \frac{2 \log{\left (x - \frac{1}{2} \right )}}{77} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{3 \log{\left (x + \frac{2}{3} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209065, size = 38, normalized size = 1.23 \[ \frac{5}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{3}{7} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{2}{77} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)*(2*x - 1)),x, algorithm="giac")
[Out]