Integrand size = 22, antiderivative size = 76 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {5764801}{15488 (1-2 x)}+\frac {231915717 x}{200000}+\frac {14171517 x^2}{25000}+\frac {2626101 x^3}{10000}+\frac {168399 x^4}{2000}+\frac {6561 x^5}{500}-\frac {1}{9453125 (3+5 x)}+\frac {79883671 \log (1-2 x)}{85184}+\frac {268 \log (3+5 x)}{103984375} \]
[Out]
Time = 0.03 (sec) , antiderivative size = 76, 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} \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {6561 x^5}{500}+\frac {168399 x^4}{2000}+\frac {2626101 x^3}{10000}+\frac {14171517 x^2}{25000}+\frac {231915717 x}{200000}+\frac {5764801}{15488 (1-2 x)}-\frac {1}{9453125 (5 x+3)}+\frac {79883671 \log (1-2 x)}{85184}+\frac {268 \log (5 x+3)}{103984375} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {231915717}{200000}+\frac {14171517 x}{12500}+\frac {7878303 x^2}{10000}+\frac {168399 x^3}{500}+\frac {6561 x^4}{100}+\frac {5764801}{7744 (-1+2 x)^2}+\frac {79883671}{42592 (-1+2 x)}+\frac {1}{1890625 (3+5 x)^2}+\frac {268}{20796875 (3+5 x)}\right ) \, dx \\ & = \frac {5764801}{15488 (1-2 x)}+\frac {231915717 x}{200000}+\frac {14171517 x^2}{25000}+\frac {2626101 x^3}{10000}+\frac {168399 x^4}{2000}+\frac {6561 x^5}{500}-\frac {1}{9453125 (3+5 x)}+\frac {79883671 \log (1-2 x)}{85184}+\frac {268 \log (3+5 x)}{103984375} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.25 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {44471943 (2+3 x)}{200000}+\frac {78921 (2+3 x)^2}{3125}+\frac {35703 (2+3 x)^3}{10000}+\frac {999 (2+3 x)^4}{2000}+\frac {27}{500} (2+3 x)^5-\frac {1351125234247+2251875390881 x}{1210000000 \left (-3+x+10 x^2\right )}+\frac {79883671 \log (3-6 x)}{85184}+\frac {268 \log (-3 (3+5 x))}{103984375} \]
[In]
[Out]
Time = 2.69 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.78
method | result | size |
default | \(\frac {6561 x^{5}}{500}+\frac {168399 x^{4}}{2000}+\frac {2626101 x^{3}}{10000}+\frac {14171517 x^{2}}{25000}+\frac {231915717 x}{200000}-\frac {1}{9453125 \left (3+5 x \right )}+\frac {268 \ln \left (3+5 x \right )}{103984375}-\frac {5764801}{15488 \left (-1+2 x \right )}+\frac {79883671 \ln \left (-1+2 x \right )}{85184}\) | \(59\) |
risch | \(\frac {6561 x^{5}}{500}+\frac {168399 x^{4}}{2000}+\frac {2626101 x^{3}}{10000}+\frac {14171517 x^{2}}{25000}+\frac {231915717 x}{200000}+\frac {-\frac {2251875390881 x}{1210000000}-\frac {1351125234247}{1210000000}}{\left (-1+2 x \right ) \left (3+5 x \right )}+\frac {79883671 \ln \left (-1+2 x \right )}{85184}+\frac {268 \ln \left (3+5 x \right )}{103984375}\) | \(62\) |
norman | \(\frac {\frac {799460529547}{15125000} x^{2}+\frac {1137481623}{100000} x^{3}+\frac {7098273}{1250} x^{4}+\frac {5341869}{2000} x^{5}+\frac {855117}{1000} x^{6}+\frac {6561}{50} x^{7}-\frac {1036728109877}{60500000}}{\left (-1+2 x \right ) \left (3+5 x \right )}+\frac {79883671 \ln \left (-1+2 x \right )}{85184}+\frac {268 \ln \left (3+5 x \right )}{103984375}\) | \(65\) |
parallelrisch | \(\frac {873269100000 x^{7}+5690803635000 x^{6}+17775069097500 x^{5}+37791205452000 x^{4}+171520 \ln \left (x +\frac {3}{5}\right ) x^{2}+62409117968750 \ln \left (x -\frac {1}{2}\right ) x^{2}+75699402010650 x^{3}-114040092086470+17152 \ln \left (x +\frac {3}{5}\right ) x +6240911796875 \ln \left (x -\frac {1}{2}\right ) x +351762633000680 x^{2}-51456 \ln \left (x +\frac {3}{5}\right )-18722735390625 \ln \left (x -\frac {1}{2}\right )}{6655000000 \left (-1+2 x \right ) \left (3+5 x \right )}\) | \(93\) |
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 79, normalized size of antiderivative = 1.04 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {1746538200000 \, x^{7} + 11381607270000 \, x^{6} + 35550138195000 \, x^{5} + 75582410904000 \, x^{4} + 151398804021300 \, x^{3} - 7200755986050 \, x^{2} + 34304 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 12481823593750 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 71072602198741 \, x - 14862377576717}{13310000000 \, {\left (10 \, x^{2} + x - 3\right )}} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.89 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {6561 x^{5}}{500} + \frac {168399 x^{4}}{2000} + \frac {2626101 x^{3}}{10000} + \frac {14171517 x^{2}}{25000} + \frac {231915717 x}{200000} + \frac {- 2251875390881 x - 1351125234247}{12100000000 x^{2} + 1210000000 x - 3630000000} + \frac {79883671 \log {\left (x - \frac {1}{2} \right )}}{85184} + \frac {268 \log {\left (x + \frac {3}{5} \right )}}{103984375} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {6561}{500} \, x^{5} + \frac {168399}{2000} \, x^{4} + \frac {2626101}{10000} \, x^{3} + \frac {14171517}{25000} \, x^{2} + \frac {231915717}{200000} \, x - \frac {2251875390881 \, x + 1351125234247}{1210000000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {268}{103984375} \, \log \left (5 \, x + 3\right ) + \frac {79883671}{85184} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 112, normalized size of antiderivative = 1.47 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=-\frac {{\left (5 \, x + 3\right )}^{5} {\left (\frac {1618458732}{5 \, x + 3} + \frac {15560361630}{{\left (5 \, x + 3\right )}^{2}} + \frac {171888467850}{{\left (5 \, x + 3\right )}^{3}} + \frac {2836763461125}{{\left (5 \, x + 3\right )}^{4}} - \frac {31204564033975}{{\left (5 \, x + 3\right )}^{5}} + 139723056\right )}}{16637500000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{9453125 \, {\left (5 \, x + 3\right )}} - \frac {4688889417}{5000000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {79883671}{85184} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.70 \[ \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx=\frac {231915717\,x}{200000}+\frac {79883671\,\ln \left (x-\frac {1}{2}\right )}{85184}+\frac {268\,\ln \left (x+\frac {3}{5}\right )}{103984375}-\frac {\frac {2251875390881\,x}{12100000000}+\frac {1351125234247}{12100000000}}{x^2+\frac {x}{10}-\frac {3}{10}}+\frac {14171517\,x^2}{25000}+\frac {2626101\,x^3}{10000}+\frac {168399\,x^4}{2000}+\frac {6561\,x^5}{500} \]
[In]
[Out]