Integrand size = 22, antiderivative size = 66 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {343}{3645 (2+3 x)^5}+\frac {931}{729 (2+3 x)^4}-\frac {11599}{2187 (2+3 x)^3}+\frac {4099}{729 (2+3 x)^2}-\frac {2180}{729 (2+3 x)}-\frac {200}{729} \log (2+3 x) \]
[Out]
Time = 0.02 (sec) , antiderivative size = 66, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {2180}{729 (3 x+2)}+\frac {4099}{729 (3 x+2)^2}-\frac {11599}{2187 (3 x+2)^3}+\frac {931}{729 (3 x+2)^4}-\frac {343}{3645 (3 x+2)^5}-\frac {200}{729} \log (3 x+2) \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{243 (2+3 x)^6}-\frac {3724}{243 (2+3 x)^5}+\frac {11599}{243 (2+3 x)^4}-\frac {8198}{243 (2+3 x)^3}+\frac {2180}{243 (2+3 x)^2}-\frac {200}{243 (2+3 x)}\right ) \, dx \\ & = -\frac {343}{3645 (2+3 x)^5}+\frac {931}{729 (2+3 x)^4}-\frac {11599}{2187 (2+3 x)^3}+\frac {4099}{729 (2+3 x)^2}-\frac {2180}{729 (2+3 x)}-\frac {200}{729} \log (2+3 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.70 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {236399+1579785 x+4264965 x^2+5403105 x^3+2648700 x^4+3000 (2+3 x)^5 \log (20+30 x)}{10935 (2+3 x)^5} \]
[In]
[Out]
Time = 2.41 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.58
method | result | size |
norman | \(\frac {-\frac {105319}{729} x -\frac {94777}{243} x^{2}-\frac {4447}{9} x^{3}-\frac {2180}{9} x^{4}-\frac {236399}{10935}}{\left (2+3 x \right )^{5}}-\frac {200 \ln \left (2+3 x \right )}{729}\) | \(38\) |
risch | \(\frac {-\frac {105319}{729} x -\frac {94777}{243} x^{2}-\frac {4447}{9} x^{3}-\frac {2180}{9} x^{4}-\frac {236399}{10935}}{\left (2+3 x \right )^{5}}-\frac {200 \ln \left (2+3 x \right )}{729}\) | \(39\) |
default | \(-\frac {343}{3645 \left (2+3 x \right )^{5}}+\frac {931}{729 \left (2+3 x \right )^{4}}-\frac {11599}{2187 \left (2+3 x \right )^{3}}+\frac {4099}{729 \left (2+3 x \right )^{2}}-\frac {2180}{729 \left (2+3 x \right )}-\frac {200 \ln \left (2+3 x \right )}{729}\) | \(55\) |
parallelrisch | \(-\frac {7776000 \ln \left (\frac {2}{3}+x \right ) x^{5}+25920000 \ln \left (\frac {2}{3}+x \right ) x^{4}-19148319 x^{5}+34560000 \ln \left (\frac {2}{3}+x \right ) x^{3}-35574930 x^{4}+23040000 \ln \left (\frac {2}{3}+x \right ) x^{2}-27470520 x^{3}+7680000 \ln \left (\frac {2}{3}+x \right ) x -11242800 x^{2}+1024000 \ln \left (\frac {2}{3}+x \right )-2060880 x}{116640 \left (2+3 x \right )^{5}}\) | \(83\) |
meijerg | \(\frac {9 x \left (\frac {81}{16} x^{4}+\frac {135}{8} x^{3}+\frac {45}{2} x^{2}+15 x +5\right )}{320 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {3 x^{2} \left (\frac {27}{8} x^{3}+\frac {45}{4} x^{2}+15 x +10\right )}{160 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {47 x^{3} \left (\frac {9}{4} x^{2}+\frac {15}{2} x +10\right )}{1920 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {69 x^{4} \left (\frac {3 x}{2}+5\right )}{640 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {3 x^{5}}{16 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {5 x \left (\frac {11097}{16} x^{4}+\frac {10395}{8} x^{3}+\frac {2115}{2} x^{2}+405 x +60\right )}{729 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {200 \ln \left (1+\frac {3 x}{2}\right )}{729}\) | \(148\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 82, normalized size of antiderivative = 1.24 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 3000 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1579785 \, x + 236399}{10935 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=- \frac {2648700 x^{4} + 5403105 x^{3} + 4264965 x^{2} + 1579785 x + 236399}{2657205 x^{5} + 8857350 x^{4} + 11809800 x^{3} + 7873200 x^{2} + 2624400 x + 349920} - \frac {200 \log {\left (3 x + 2 \right )}}{729} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} - \frac {200}{729} \, \log \left (3 \, x + 2\right ) \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.59 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \, {\left (3 \, x + 2\right )}^{5}} - \frac {200}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
[In]
[Out]
Time = 1.31 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx=-\frac {200\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {2180\,x^4}{2187}+\frac {4447\,x^3}{2187}+\frac {94777\,x^2}{59049}+\frac {105319\,x}{177147}+\frac {236399}{2657205}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
[In]
[Out]