Integrand size = 20, antiderivative size = 76 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=\frac {1}{105 (2+3 x)^5}-\frac {11}{196 (2+3 x)^4}-\frac {22}{1029 (2+3 x)^3}-\frac {22}{2401 (2+3 x)^2}-\frac {88}{16807 (2+3 x)}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \log (2+3 x)}{117649} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 76, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=-\frac {88}{16807 (3 x+2)}-\frac {22}{2401 (3 x+2)^2}-\frac {22}{1029 (3 x+2)^3}-\frac {11}{196 (3 x+2)^4}+\frac {1}{105 (3 x+2)^5}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \log (3 x+2)}{117649} \]
[In]
[Out]
Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {352}{117649 (-1+2 x)}-\frac {1}{7 (2+3 x)^6}+\frac {33}{49 (2+3 x)^5}+\frac {66}{343 (2+3 x)^4}+\frac {132}{2401 (2+3 x)^3}+\frac {264}{16807 (2+3 x)^2}+\frac {528}{117649 (2+3 x)}\right ) \, dx \\ & = \frac {1}{105 (2+3 x)^5}-\frac {11}{196 (2+3 x)^4}-\frac {22}{1029 (2+3 x)^3}-\frac {22}{2401 (2+3 x)^2}-\frac {88}{16807 (2+3 x)}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \log (2+3 x)}{117649} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.66 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=\frac {-\frac {7 \left (348226+1268025 x+1833480 x^2+1389960 x^3+427680 x^4\right )}{(2+3 x)^5}-10560 \log (3-6 x)+10560 \log (2+3 x)}{7058940} \]
[In]
[Out]
Time = 2.50 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.61
method | result | size |
norman | \(\frac {-\frac {84535}{67228} x -\frac {30558}{16807} x^{2}-\frac {23166}{16807} x^{3}-\frac {7128}{16807} x^{4}-\frac {174113}{504210}}{\left (2+3 x \right )^{5}}-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(46\) |
risch | \(\frac {-\frac {84535}{67228} x -\frac {30558}{16807} x^{2}-\frac {23166}{16807} x^{3}-\frac {7128}{16807} x^{4}-\frac {174113}{504210}}{\left (2+3 x \right )^{5}}-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(47\) |
default | \(-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {1}{105 \left (2+3 x \right )^{5}}-\frac {11}{196 \left (2+3 x \right )^{4}}-\frac {22}{1029 \left (2+3 x \right )^{3}}-\frac {22}{2401 \left (2+3 x \right )^{2}}-\frac {88}{16807 \left (2+3 x \right )}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
parallelrisch | \(\frac {13685760 \ln \left (\frac {2}{3}+x \right ) x^{5}-13685760 \ln \left (x -\frac {1}{2}\right ) x^{5}+45619200 \ln \left (\frac {2}{3}+x \right ) x^{4}-45619200 \ln \left (x -\frac {1}{2}\right ) x^{4}+98722071 x^{5}+60825600 \ln \left (\frac {2}{3}+x \right ) x^{3}-60825600 \ln \left (x -\frac {1}{2}\right ) x^{3}+313106850 x^{4}+40550400 \ln \left (\frac {2}{3}+x \right ) x^{2}-40550400 \ln \left (x -\frac {1}{2}\right ) x^{2}+386872920 x^{3}+13516800 \ln \left (\frac {2}{3}+x \right ) x -13516800 \ln \left (x -\frac {1}{2}\right ) x +224059920 x^{2}+1802240 \ln \left (\frac {2}{3}+x \right )-1802240 \ln \left (x -\frac {1}{2}\right )+50163680 x}{37647680 \left (2+3 x \right )^{5}}\) | \(132\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.51 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=-\frac {2993760 \, x^{4} + 9729720 \, x^{3} + 12834360 \, x^{2} - 10560 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 10560 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 8876175 \, x + 2437582}{7058940 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.86 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=- \frac {427680 x^{4} + 1389960 x^{3} + 1833480 x^{2} + 1268025 x + 348226}{245046060 x^{5} + 816820200 x^{4} + 1089093600 x^{3} + 726062400 x^{2} + 242020800 x + 32269440} - \frac {176 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {176 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.87 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=-\frac {427680 \, x^{4} + 1389960 \, x^{3} + 1833480 \, x^{2} + 1268025 \, x + 348226}{1008420 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {176}{117649} \, \log \left (3 \, x + 2\right ) - \frac {176}{117649} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.63 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=-\frac {427680 \, x^{4} + 1389960 \, x^{3} + 1833480 \, x^{2} + 1268025 \, x + 348226}{1008420 \, {\left (3 \, x + 2\right )}^{5}} + \frac {176}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {176}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
[In]
[Out]
Time = 1.41 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.74 \[ \int \frac {3+5 x}{(1-2 x) (2+3 x)^6} \, dx=\frac {352\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}-\frac {\frac {88\,x^4}{50421}+\frac {286\,x^3}{50421}+\frac {10186\,x^2}{1361367}+\frac {84535\,x}{16336404}+\frac {174113}{122523030}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
[In]
[Out]