Integrand size = 22, antiderivative size = 64 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {8}{3773 (1-2 x)}+\frac {9}{98 (2+3 x)^2}+\frac {351}{343 (2+3 x)}-\frac {1072 \log (1-2 x)}{290521}-\frac {12393 \log (2+3 x)}{2401}+\frac {625}{121} \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 64, 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} \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {8}{3773 (1-2 x)}+\frac {351}{343 (3 x+2)}+\frac {9}{98 (3 x+2)^2}-\frac {1072 \log (1-2 x)}{290521}-\frac {12393 \log (3 x+2)}{2401}+\frac {625}{121} \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {16}{3773 (-1+2 x)^2}-\frac {2144}{290521 (-1+2 x)}-\frac {27}{49 (2+3 x)^3}-\frac {1053}{343 (2+3 x)^2}-\frac {37179}{2401 (2+3 x)}+\frac {3125}{121 (3+5 x)}\right ) \, dx \\ & = \frac {8}{3773 (1-2 x)}+\frac {9}{98 (2+3 x)^2}+\frac {351}{343 (2+3 x)}-\frac {1072 \log (1-2 x)}{290521}-\frac {12393 \log (2+3 x)}{2401}+\frac {625}{121} \log (3+5 x) \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.95 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {-2144 \log (5-10 x)-2999106 \log (5 (2+3 x))+7 \left (\frac {176}{1-2 x}+\frac {7623}{(2+3 x)^2}+\frac {84942}{2+3 x}+428750 \log (3+5 x)\right )}{581042} \]
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Time = 2.68 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.81
method | result | size |
risch | \(\frac {\frac {23094}{3773} x^{2}+\frac {4458}{3773} x -\frac {16201}{7546}}{\left (-1+2 x \right ) \left (2+3 x \right )^{2}}-\frac {1072 \ln \left (-1+2 x \right )}{290521}-\frac {12393 \ln \left (2+3 x \right )}{2401}+\frac {625 \ln \left (3+5 x \right )}{121}\) | \(52\) |
default | \(\frac {625 \ln \left (3+5 x \right )}{121}-\frac {8}{3773 \left (-1+2 x \right )}-\frac {1072 \ln \left (-1+2 x \right )}{290521}+\frac {9}{98 \left (2+3 x \right )^{2}}+\frac {351}{343 \left (2+3 x \right )}-\frac {12393 \ln \left (2+3 x \right )}{2401}\) | \(53\) |
norman | \(\frac {\frac {79623}{7546} x^{2}+\frac {20061}{3773} x^{3}-\frac {25117}{7546}}{\left (-1+2 x \right ) \left (2+3 x \right )^{2}}-\frac {1072 \ln \left (-1+2 x \right )}{290521}-\frac {12393 \ln \left (2+3 x \right )}{2401}+\frac {625 \ln \left (3+5 x \right )}{121}\) | \(53\) |
parallelrisch | \(-\frac {215935632 \ln \left (\frac {2}{3}+x \right ) x^{3}-216090000 \ln \left (x +\frac {3}{5}\right ) x^{3}+154368 \ln \left (x -\frac {1}{2}\right ) x^{3}+179946360 \ln \left (\frac {2}{3}+x \right ) x^{2}-180075000 \ln \left (x +\frac {3}{5}\right ) x^{2}+128640 \ln \left (x -\frac {1}{2}\right ) x^{2}+22454586 x^{3}-47985696 \ln \left (\frac {2}{3}+x \right ) x +48020000 \ln \left (x +\frac {3}{5}\right ) x -34304 \ln \left (x -\frac {1}{2}\right ) x +4486251 x^{2}-47985696 \ln \left (\frac {2}{3}+x \right )+48020000 \ln \left (x +\frac {3}{5}\right )-34304 \ln \left (x -\frac {1}{2}\right )-7736036 x}{2324168 \left (-1+2 x \right ) \left (2+3 x \right )^{2}}\) | \(124\) |
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Time = 0.22 (sec) , antiderivative size = 98, normalized size of antiderivative = 1.53 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {3556476 \, x^{2} + 3001250 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (5 \, x + 3\right ) - 2999106 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 2144 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 686532 \, x - 1247477}{581042 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]
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Time = 0.10 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {46188 x^{2} + 8916 x - 16201}{135828 x^{3} + 113190 x^{2} - 30184 x - 30184} - \frac {1072 \log {\left (x - \frac {1}{2} \right )}}{290521} + \frac {625 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {12393 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
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Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {46188 \, x^{2} + 8916 \, x - 16201}{7546 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac {625}{121} \, \log \left (5 \, x + 3\right ) - \frac {12393}{2401} \, \log \left (3 \, x + 2\right ) - \frac {1072}{290521} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.03 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=-\frac {8}{3773 \, {\left (2 \, x - 1\right )}} - \frac {54 \, {\left (\frac {287}{2 \, x - 1} + 120\right )}}{2401 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{2}} - \frac {12393}{2401} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) + \frac {625}{121} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
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Time = 1.19 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.75 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx=\frac {625\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {12393\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {1072\,\ln \left (x-\frac {1}{2}\right )}{290521}-\frac {\frac {1283\,x^2}{3773}+\frac {743\,x}{11319}-\frac {16201}{135828}}{-x^3-\frac {5\,x^2}{6}+\frac {2\,x}{9}+\frac {2}{9}} \]
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