Integrand size = 23, antiderivative size = 32 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=-\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x) \]
[Out]
Time = 0.02 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {907} \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=-\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (2 x+3) \]
[In]
[Out]
Rule 907
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {9}{16 (-1+2 x)^2}+\frac {41}{64 (-1+2 x)}-\frac {25}{64 (3+2 x)}\right ) \, dx \\ & = -\frac {9}{32 (1-2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=\frac {9}{32 (-1+2 x)}+\frac {41}{128} \log (1-2 x)-\frac {25}{128} \log (3+2 x) \]
[In]
[Out]
Time = 0.17 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.78
method | result | size |
risch | \(\frac {9}{64 \left (x -\frac {1}{2}\right )}-\frac {25 \ln \left (3+2 x \right )}{128}+\frac {41 \ln \left (2 x -1\right )}{128}\) | \(25\) |
default | \(-\frac {25 \ln \left (3+2 x \right )}{128}+\frac {9}{32 \left (2 x -1\right )}+\frac {41 \ln \left (2 x -1\right )}{128}\) | \(27\) |
norman | \(\frac {9 x}{16 \left (2 x -1\right )}-\frac {25 \ln \left (3+2 x \right )}{128}+\frac {41 \ln \left (2 x -1\right )}{128}\) | \(28\) |
parallelrisch | \(\frac {82 \ln \left (x -\frac {1}{2}\right ) x -50 \ln \left (\frac {3}{2}+x \right ) x -41 \ln \left (x -\frac {1}{2}\right )+25 \ln \left (\frac {3}{2}+x \right )+72 x}{256 x -128}\) | \(40\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=-\frac {25 \, {\left (2 \, x - 1\right )} \log \left (2 \, x + 3\right ) - 41 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36}{128 \, {\left (2 \, x - 1\right )}} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=\frac {41 \log {\left (x - \frac {1}{2} \right )}}{128} - \frac {25 \log {\left (x + \frac {3}{2} \right )}}{128} + \frac {9}{64 x - 32} \]
[In]
[Out]
none
Time = 0.23 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=\frac {9}{32 \, {\left (2 \, x - 1\right )}} - \frac {25}{128} \, \log \left (2 \, x + 3\right ) + \frac {41}{128} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=\frac {9}{32 \, {\left (2 \, x - 1\right )}} - \frac {1}{8} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) - \frac {25}{128} \, \log \left ({\left | -\frac {4}{2 \, x - 1} - 1 \right |}\right ) \]
[In]
[Out]
Time = 0.11 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.69 \[ \int \frac {-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx=\frac {41\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {25\,\ln \left (x+\frac {3}{2}\right )}{128}+\frac {9}{64\,\left (x-\frac {1}{2}\right )} \]
[In]
[Out]