Optimal. Leaf size=32 \[ \frac {7}{22 (1-2 x)}-\frac {1}{121} \log (1-2 x)+\frac {1}{121} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
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} \[ \frac {7}{22 (1-2 x)}-\frac {1}{121} \log (1-2 x)+\frac {1}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {7}{11 (-1+2 x)^2}-\frac {2}{121 (-1+2 x)}+\frac {5}{121 (3+5 x)}\right ) \, dx\\ &=\frac {7}{22 (1-2 x)}-\frac {1}{121} \log (1-2 x)+\frac {1}{121} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 37, normalized size = 1.16 \[ \frac {(2-4 x) \log (1-2 x)+(4 x-2) \log (10 x+6)-77}{242 (2 x-1)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.58, size = 37, normalized size = 1.16 \[ \frac {2 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 2 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 77}{242 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.14, size = 25, normalized size = 0.78 \[ -\frac {7}{22 \, {\left (2 \, x - 1\right )}} + \frac {1}{121} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ -\frac {\ln \left (2 x -1\right )}{121}+\frac {\ln \left (5 x +3\right )}{121}-\frac {7}{22 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 26, normalized size = 0.81 \[ -\frac {7}{22 \, {\left (2 \, x - 1\right )}} + \frac {1}{121} \, \log \left (5 \, x + 3\right ) - \frac {1}{121} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.07, size = 18, normalized size = 0.56 \[ \frac {2\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{121}-\frac {7}{44\,\left (x-\frac {1}{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 22, normalized size = 0.69 \[ - \frac {\log {\left (x - \frac {1}{2} \right )}}{121} + \frac {\log {\left (x + \frac {3}{5} \right )}}{121} - \frac {7}{44 x - 22} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________