Integrand size = 22, antiderivative size = 109 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=\frac {3872}{5764801 (1-2 x)}-\frac {1}{1029 (2+3 x)^7}+\frac {11}{1029 (2+3 x)^6}-\frac {319}{12005 (2+3 x)^5}-\frac {341}{16807 (2+3 x)^4}-\frac {4180}{352947 (2+3 x)^3}-\frac {5632}{823543 (2+3 x)^2}-\frac {4048}{823543 (2+3 x)}-\frac {68288 \log (1-2 x)}{40353607}+\frac {68288 \log (2+3 x)}{40353607} \]
[Out]
Time = 0.04 (sec) , antiderivative size = 109, 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} \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=\frac {3872}{5764801 (1-2 x)}-\frac {4048}{823543 (3 x+2)}-\frac {5632}{823543 (3 x+2)^2}-\frac {4180}{352947 (3 x+2)^3}-\frac {341}{16807 (3 x+2)^4}-\frac {319}{12005 (3 x+2)^5}+\frac {11}{1029 (3 x+2)^6}-\frac {1}{1029 (3 x+2)^7}-\frac {68288 \log (1-2 x)}{40353607}+\frac {68288 \log (3 x+2)}{40353607} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {7744}{5764801 (-1+2 x)^2}-\frac {136576}{40353607 (-1+2 x)}+\frac {1}{49 (2+3 x)^8}-\frac {66}{343 (2+3 x)^7}+\frac {957}{2401 (2+3 x)^6}+\frac {4092}{16807 (2+3 x)^5}+\frac {12540}{117649 (2+3 x)^4}+\frac {33792}{823543 (2+3 x)^3}+\frac {12144}{823543 (2+3 x)^2}+\frac {204864}{40353607 (2+3 x)}\right ) \, dx \\ & = \frac {3872}{5764801 (1-2 x)}-\frac {1}{1029 (2+3 x)^7}+\frac {11}{1029 (2+3 x)^6}-\frac {319}{12005 (2+3 x)^5}-\frac {341}{16807 (2+3 x)^4}-\frac {4180}{352947 (2+3 x)^3}-\frac {5632}{823543 (2+3 x)^2}-\frac {4048}{823543 (2+3 x)}-\frac {68288 \log (1-2 x)}{40353607}+\frac {68288 \log (2+3 x)}{40353607} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.68 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=\frac {16 \left (-\frac {7 \left (-76539293-327016403 x-183177225 x^2+1495734471 x^3+4176440730 x^4+5057708040 x^5+3049144560 x^6+746729280 x^7\right )}{16 (-1+2 x) (2+3 x)^7}-64020 \log (1-2 x)+64020 \log (4+6 x)\right )}{605304105} \]
[In]
[Out]
Time = 2.65 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.62
method | result | size |
norman | \(\frac {-\frac {71225451}{4117715} x^{3}-\frac {49781952}{5764801} x^{7}-\frac {48168648}{823543} x^{5}-\frac {39775626}{823543} x^{4}-\frac {4148496}{117649} x^{6}+\frac {1744545}{823543} x^{2}+\frac {46716629}{12353145} x +\frac {76539293}{86472015}}{\left (-1+2 x \right ) \left (2+3 x \right )^{7}}-\frac {68288 \ln \left (-1+2 x \right )}{40353607}+\frac {68288 \ln \left (2+3 x \right )}{40353607}\) | \(68\) |
risch | \(\frac {-\frac {71225451}{4117715} x^{3}-\frac {49781952}{5764801} x^{7}-\frac {48168648}{823543} x^{5}-\frac {39775626}{823543} x^{4}-\frac {4148496}{117649} x^{6}+\frac {1744545}{823543} x^{2}+\frac {46716629}{12353145} x +\frac {76539293}{86472015}}{\left (-1+2 x \right ) \left (2+3 x \right )^{7}}-\frac {68288 \ln \left (-1+2 x \right )}{40353607}+\frac {68288 \ln \left (2+3 x \right )}{40353607}\) | \(69\) |
default | \(-\frac {3872}{5764801 \left (-1+2 x \right )}-\frac {68288 \ln \left (-1+2 x \right )}{40353607}-\frac {1}{1029 \left (2+3 x \right )^{7}}+\frac {11}{1029 \left (2+3 x \right )^{6}}-\frac {319}{12005 \left (2+3 x \right )^{5}}-\frac {341}{16807 \left (2+3 x \right )^{4}}-\frac {4180}{352947 \left (2+3 x \right )^{3}}-\frac {5632}{823543 \left (2+3 x \right )^{2}}-\frac {4048}{823543 \left (2+3 x \right )}+\frac {68288 \ln \left (2+3 x \right )}{40353607}\) | \(90\) |
parallelrisch | \(\frac {-96638852800 x -132161863680 \ln \left (\frac {2}{3}+x \right ) x^{3}-146846515200 \ln \left (\frac {2}{3}+x \right ) x^{2}-47550300160 \ln \left (\frac {2}{3}+x \right ) x +2944936522836 x^{5}+4557442328586 x^{6}+3031810289865 x^{7}-986787280080 x^{3}+102789497160 x^{4}-545359125920 x^{2}+781160024358 x^{8}-330404659200 \ln \left (x -\frac {1}{2}\right ) x^{4}+330404659200 \ln \left (\frac {2}{3}+x \right ) x^{4}-5594152960 \ln \left (\frac {2}{3}+x \right )+132161863680 \ln \left (x -\frac {1}{2}\right ) x^{3}+796511232000 \ln \left (\frac {2}{3}+x \right ) x^{7}+146846515200 \ln \left (x -\frac {1}{2}\right ) x^{2}+47550300160 \ln \left (x -\frac {1}{2}\right ) x +1090335375360 \ln \left (\frac {2}{3}+x \right ) x^{5}+1338138869760 \ln \left (\frac {2}{3}+x \right ) x^{6}-191162695680 \ln \left (x -\frac {1}{2}\right ) x^{8}+5594152960 \ln \left (x -\frac {1}{2}\right )+191162695680 \ln \left (\frac {2}{3}+x \right ) x^{8}-796511232000 \ln \left (x -\frac {1}{2}\right ) x^{7}-1338138869760 \ln \left (x -\frac {1}{2}\right ) x^{6}-1090335375360 \ln \left (x -\frac {1}{2}\right ) x^{5}}{25826308480 \left (-1+2 x \right ) \left (2+3 x \right )^{7}}\) | \(208\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 175, normalized size of antiderivative = 1.61 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=-\frac {5227104960 \, x^{7} + 21344011920 \, x^{6} + 35403956280 \, x^{5} + 29235085110 \, x^{4} + 10470141297 \, x^{3} - 1282240575 \, x^{2} - 1024320 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (3 \, x + 2\right ) + 1024320 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (2 \, x - 1\right ) - 2289114821 \, x - 535775051}{605304105 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 95, normalized size of antiderivative = 0.87 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=\frac {- 746729280 x^{7} - 3049144560 x^{6} - 5057708040 x^{5} - 4176440730 x^{4} - 1495734471 x^{3} + 183177225 x^{2} + 327016403 x + 76539293}{378228593610 x^{8} + 1575952473375 x^{7} + 2647600155270 x^{6} + 2157303830220 x^{5} + 653728433400 x^{4} - 261491373360 x^{3} - 290545970400 x^{2} - 94081552320 x - 11068417920} - \frac {68288 \log {\left (x - \frac {1}{2} \right )}}{40353607} + \frac {68288 \log {\left (x + \frac {2}{3} \right )}}{40353607} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 96, normalized size of antiderivative = 0.88 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=-\frac {746729280 \, x^{7} + 3049144560 \, x^{6} + 5057708040 \, x^{5} + 4176440730 \, x^{4} + 1495734471 \, x^{3} - 183177225 \, x^{2} - 327016403 \, x - 76539293}{86472015 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} + \frac {68288}{40353607} \, \log \left (3 \, x + 2\right ) - \frac {68288}{40353607} \, \log \left (2 \, x - 1\right ) \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 96, normalized size of antiderivative = 0.88 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=-\frac {3872}{5764801 \, {\left (2 \, x - 1\right )}} + \frac {16 \, {\left (\frac {6995041011}{2 \, x - 1} + \frac {43950177747}{{\left (2 \, x - 1\right )}^{2}} + \frac {148454802405}{{\left (2 \, x - 1\right )}^{3}} + \frac {284722344900}{{\left (2 \, x - 1\right )}^{4}} + \frac {294251913900}{{\left (2 \, x - 1\right )}^{5}} + \frac {128036230210}{{\left (2 \, x - 1\right )}^{6}} + 466999587\right )}}{1412376245 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{7}} + \frac {68288}{40353607} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 86, normalized size of antiderivative = 0.79 \[ \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx=\frac {136576\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{40353607}-\frac {\frac {34144\,x^7}{17294403}+\frac {8536\,x^6}{1058841}+\frac {892012\,x^5}{66706983}+\frac {2209757\,x^4}{200120949}+\frac {7913939\,x^3}{2001209490}-\frac {581515\,x^2}{1200725694}-\frac {46716629\,x}{54032656230}-\frac {76539293}{378228593610}}{x^8+\frac {25\,x^7}{6}+7\,x^6+\frac {154\,x^5}{27}+\frac {140\,x^4}{81}-\frac {56\,x^3}{81}-\frac {560\,x^2}{729}-\frac {544\,x}{2187}-\frac {64}{2187}} \]
[In]
[Out]