Optimal. Leaf size=32 \[ \frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \log (3 x+2) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^2 (2+3 x)} \, dx &=\int \left (\frac {11}{7 (-1+2 x)^2}+\frac {2}{49 (-1+2 x)}-\frac {3}{49 (2+3 x)}\right ) \, dx\\ &=\frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 37, normalized size = 1.16 \begin {gather*} \frac {(4 x-2) \log (1-2 x)+(2-4 x) \log (6 x+4)-77}{98 (2 x-1)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3+5 x}{(1-2 x)^2 (2+3 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.47, size = 37, normalized size = 1.16 \begin {gather*} -\frac {2 \, {\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) - 2 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) + 77}{98 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.03, size = 25, normalized size = 0.78 \begin {gather*} -\frac {11}{14 \, {\left (2 \, x - 1\right )}} - \frac {1}{49} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 27, normalized size = 0.84 \begin {gather*} \frac {\ln \left (2 x -1\right )}{49}-\frac {\ln \left (3 x +2\right )}{49}-\frac {11}{14 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.54, size = 26, normalized size = 0.81 \begin {gather*} -\frac {11}{14 \, {\left (2 \, x - 1\right )}} - \frac {1}{49} \, \log \left (3 \, x + 2\right ) + \frac {1}{49} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 18, normalized size = 0.56 \begin {gather*} -\frac {2\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{49}-\frac {11}{28\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 22, normalized size = 0.69 \begin {gather*} \frac {\log {\left (x - \frac {1}{2} \right )}}{49} - \frac {\log {\left (x + \frac {2}{3} \right )}}{49} - \frac {11}{28 x - 14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________