Optimal. Leaf size=31 \[ -\frac {2}{77} \log (1-2 x)-\frac {3}{7} \log (3 x+2)+\frac {5}{11} \log (5 x+3) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {72} \begin {gather*} -\frac {2}{77} \log (1-2 x)-\frac {3}{7} \log (3 x+2)+\frac {5}{11} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x) (3+5 x)} \, dx &=\int \left (-\frac {4}{77 (-1+2 x)}-\frac {9}{7 (2+3 x)}+\frac {25}{11 (3+5 x)}\right ) \, dx\\ &=-\frac {2}{77} \log (1-2 x)-\frac {3}{7} \log (2+3 x)+\frac {5}{11} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \begin {gather*} -\frac {2}{77} \log (1-2 x)-\frac {3}{7} \log (3 x+2)+\frac {5}{11} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(1-2 x) (2+3 x) (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.38, size = 25, normalized size = 0.81 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.90, size = 28, normalized size = 0.90 \begin {gather*} \frac {5}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {3}{7} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {2}{77} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 26, normalized size = 0.84 \begin {gather*} -\frac {2 \ln \left (2 x -1\right )}{77}-\frac {3 \ln \left (3 x +2\right )}{7}+\frac {5 \ln \left (5 x +3\right )}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 25, normalized size = 0.81 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.19, size = 19, normalized size = 0.61 \begin {gather*} \frac {5\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {3\,\ln \left (x+\frac {2}{3}\right )}{7}-\frac {2\,\ln \left (x-\frac {1}{2}\right )}{77} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 29, normalized size = 0.94 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________