Integrand size = 22, antiderivative size = 50 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {343}{18 (2+3 x)^2}-\frac {3136}{9 (2+3 x)}-\frac {1331}{5 (3+5 x)}+2541 \log (2+3 x)-2541 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 50, 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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {3136}{9 (3 x+2)}-\frac {1331}{5 (5 x+3)}-\frac {343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{3 (2+3 x)^3}+\frac {3136}{3 (2+3 x)^2}+\frac {7623}{2+3 x}+\frac {1331}{(3+5 x)^2}-\frac {12705}{3+5 x}\right ) \, dx \\ & = -\frac {343}{18 (2+3 x)^2}-\frac {3136}{9 (2+3 x)}-\frac {1331}{5 (3+5 x)}+2541 \log (2+3 x)-2541 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {289137+891911 x+686022 x^2}{90 (2+3 x)^2 (3+5 x)}+2541 \log (5 (2+3 x))-2541 \log (3+5 x) \]
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Time = 2.46 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.88
method | result | size |
risch | \(\frac {-\frac {114337}{15} x^{2}-\frac {891911}{90} x -\frac {96379}{30}}{\left (2+3 x \right )^{2} \left (3+5 x \right )}+2541 \ln \left (2+3 x \right )-2541 \ln \left (3+5 x \right )\) | \(44\) |
default | \(-\frac {343}{18 \left (2+3 x \right )^{2}}-\frac {3136}{9 \left (2+3 x \right )}-\frac {1331}{5 \left (3+5 x \right )}+2541 \ln \left (2+3 x \right )-2541 \ln \left (3+5 x \right )\) | \(45\) |
norman | \(\frac {\frac {96379}{8} x^{3}+\frac {125353}{8} x^{2}+\frac {30493}{6} x}{\left (2+3 x \right )^{2} \left (3+5 x \right )}+2541 \ln \left (2+3 x \right )-2541 \ln \left (3+5 x \right )\) | \(47\) |
parallelrisch | \(\frac {2744280 \ln \left (\frac {2}{3}+x \right ) x^{3}-2744280 \ln \left (x +\frac {3}{5}\right ) x^{3}+5305608 \ln \left (\frac {2}{3}+x \right ) x^{2}-5305608 \ln \left (x +\frac {3}{5}\right ) x^{2}+289137 x^{3}+3415104 \ln \left (\frac {2}{3}+x \right ) x -3415104 \ln \left (x +\frac {3}{5}\right ) x +376059 x^{2}+731808 \ln \left (\frac {2}{3}+x \right )-731808 \ln \left (x +\frac {3}{5}\right )+121972 x}{24 \left (2+3 x \right )^{2} \left (3+5 x \right )}\) | \(93\) |
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Time = 0.22 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.50 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {686022 \, x^{2} + 228690 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 228690 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 891911 \, x + 289137}{90 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=- \frac {686022 x^{2} + 891911 x + 289137}{4050 x^{3} + 7830 x^{2} + 5040 x + 1080} - 2541 \log {\left (x + \frac {3}{5} \right )} + 2541 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.21 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {686022 \, x^{2} + 891911 \, x + 289137}{90 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 2541 \, \log \left (5 \, x + 3\right ) + 2541 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=-\frac {1331}{5 \, {\left (5 \, x + 3\right )}} + \frac {245 \, {\left (\frac {66}{5 \, x + 3} + 163\right )}}{2 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + 2541 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx=5082\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {114337\,x^2}{675}+\frac {891911\,x}{4050}+\frac {96379}{1350}}{x^3+\frac {29\,x^2}{15}+\frac {56\,x}{45}+\frac {4}{15}} \]
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