Integrand size = 22, antiderivative size = 59 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {16807}{10648 (1-2 x)}+\frac {243 x}{500}-\frac {1}{151250 (3+5 x)^2}-\frac {169}{831875 (3+5 x)}+\frac {36015 \log (1-2 x)}{29282}+\frac {11562 \log (3+5 x)}{9150625} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {243 x}{500}+\frac {16807}{10648 (1-2 x)}-\frac {169}{831875 (5 x+3)}-\frac {1}{151250 (5 x+3)^2}+\frac {36015 \log (1-2 x)}{29282}+\frac {11562 \log (5 x+3)}{9150625} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {243}{500}+\frac {16807}{5324 (-1+2 x)^2}+\frac {36015}{14641 (-1+2 x)}+\frac {1}{15125 (3+5 x)^3}+\frac {169}{166375 (3+5 x)^2}+\frac {11562}{1830125 (3+5 x)}\right ) \, dx \\ & = \frac {16807}{10648 (1-2 x)}+\frac {243 x}{500}-\frac {1}{151250 (3+5 x)^2}-\frac {169}{831875 (3+5 x)}+\frac {36015 \log (1-2 x)}{29282}+\frac {11562 \log (3+5 x)}{9150625} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.93 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {\frac {115548125}{1-2 x}+17788815 (-1+2 x)-\frac {484}{(3+5 x)^2}-\frac {14872}{3+5 x}+90037500 \log (1-2 x)+92496 \log (6+10 x)}{73205000} \]
[In]
[Out]
Time = 0.89 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.80
method | result | size |
risch | \(\frac {243 x}{500}+\frac {-\frac {52524579}{1331000} x^{2}-\frac {31513269}{665500} x -\frac {3781411}{266200}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {36015 \ln \left (-1+2 x \right )}{29282}+\frac {11562 \ln \left (3+5 x \right )}{9150625}\) | \(47\) |
default | \(\frac {243 x}{500}-\frac {1}{151250 \left (3+5 x \right )^{2}}-\frac {169}{831875 \left (3+5 x \right )}+\frac {11562 \ln \left (3+5 x \right )}{9150625}-\frac {16807}{10648 \left (-1+2 x \right )}+\frac {36015 \ln \left (-1+2 x \right )}{29282}\) | \(48\) |
norman | \(\frac {-\frac {150541208}{1497375} x^{2}-\frac {18539749}{299475} x^{3}-\frac {16364597}{499125} x +\frac {243}{10} x^{4}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {36015 \ln \left (-1+2 x \right )}{29282}+\frac {11562 \ln \left (3+5 x \right )}{9150625}\) | \(52\) |
parallelrisch | \(\frac {10405800 \ln \left (x +\frac {3}{5}\right ) x^{3}+10129218750 \ln \left (x -\frac {1}{2}\right ) x^{3}+4002483375 x^{4}+7284060 \ln \left (x +\frac {3}{5}\right ) x^{2}+7090453125 \ln \left (x -\frac {1}{2}\right ) x^{2}-10196861950 x^{3}-2497392 \ln \left (x +\frac {3}{5}\right ) x -2431012500 \ln \left (x -\frac {1}{2}\right ) x -16559532880 x^{2}-1873044 \ln \left (x +\frac {3}{5}\right )-1823259375 \ln \left (x -\frac {1}{2}\right )-5400317010 x}{164711250 \left (-1+2 x \right ) \left (3+5 x \right )^{2}}\) | \(98\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 85, normalized size of antiderivative = 1.44 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {1778881500 \, x^{4} + 1245217050 \, x^{3} - 3315783405 \, x^{2} + 92496 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 90037500 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 3786658260 \, x - 1039888025}{73205000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.86 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {243 x}{500} + \frac {- 52524579 x^{2} - 63026538 x - 18907055}{66550000 x^{3} + 46585000 x^{2} - 15972000 x - 11979000} + \frac {36015 \log {\left (x - \frac {1}{2} \right )}}{29282} + \frac {11562 \log {\left (x + \frac {3}{5} \right )}}{9150625} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {243}{500} \, x - \frac {52524579 \, x^{2} + 63026538 \, x + 18907055}{1331000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {11562}{9150625} \, \log \left (5 \, x + 3\right ) + \frac {36015}{29282} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 83, normalized size of antiderivative = 1.41 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {{\left (2 \, x - 1\right )} {\left (\frac {391367530}{2 \, x - 1} + \frac {430519419}{{\left (2 \, x - 1\right )}^{2}} + 88944075\right )}}{14641000 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} - \frac {16807}{10648 \, {\left (2 \, x - 1\right )}} - \frac {1539}{1250} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {11562}{9150625} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
[In]
[Out]
Time = 1.18 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx=\frac {243\,x}{500}+\frac {36015\,\ln \left (x-\frac {1}{2}\right )}{29282}+\frac {11562\,\ln \left (x+\frac {3}{5}\right )}{9150625}+\frac {\frac {52524579\,x^2}{66550000}+\frac {31513269\,x}{33275000}+\frac {3781411}{13310000}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}} \]
[In]
[Out]