Integrand size = 20, antiderivative size = 41 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {3773}{32 (1-2 x)}+\frac {3177 x}{16}+\frac {243 x^2}{4}+\frac {45 x^3}{4}+\frac {3283}{16} \log (1-2 x) \]
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Time = 0.01 (sec) , antiderivative size = 41, 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} \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {45 x^3}{4}+\frac {243 x^2}{4}+\frac {3177 x}{16}+\frac {3773}{32 (1-2 x)}+\frac {3283}{16} \log (1-2 x) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {3177}{16}+\frac {243 x}{2}+\frac {135 x^2}{4}+\frac {3773}{16 (-1+2 x)^2}+\frac {3283}{8 (-1+2 x)}\right ) \, dx \\ & = \frac {3773}{32 (1-2 x)}+\frac {3177 x}{16}+\frac {243 x^2}{4}+\frac {45 x^3}{4}+\frac {3283}{16} \log (1-2 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.00 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {-65-13770 x+10764 x^2+3528 x^3+720 x^4+6566 (-1+2 x) \log (1-2 x)}{-32+64 x} \]
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Time = 2.60 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.73
method | result | size |
risch | \(\frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}-\frac {3773}{64 \left (x -\frac {1}{2}\right )}+\frac {3283 \ln \left (-1+2 x \right )}{16}\) | \(30\) |
default | \(\frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}+\frac {3283 \ln \left (-1+2 x \right )}{16}-\frac {3773}{32 \left (-1+2 x \right )}\) | \(32\) |
norman | \(\frac {-\frac {3475}{8} x +\frac {2691}{8} x^{2}+\frac {441}{4} x^{3}+\frac {45}{2} x^{4}}{-1+2 x}+\frac {3283 \ln \left (-1+2 x \right )}{16}\) | \(37\) |
parallelrisch | \(\frac {360 x^{4}+1764 x^{3}+6566 \ln \left (x -\frac {1}{2}\right ) x +5382 x^{2}-3283 \ln \left (x -\frac {1}{2}\right )-6950 x}{-16+32 x}\) | \(42\) |
meijerg | \(\frac {98 x}{1-2 x}+\frac {3283 \ln \left (1-2 x \right )}{16}+\frac {57 x \left (-6 x +6\right )}{2 \left (1-2 x \right )}+\frac {351 x \left (-8 x^{2}-12 x +12\right )}{32 \left (1-2 x \right )}+\frac {9 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{16 \left (1-2 x \right )}\) | \(80\) |
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Time = 0.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.02 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 6354 \, x - 3773}{32 \, {\left (2 \, x - 1\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.83 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {45 x^{3}}{4} + \frac {243 x^{2}}{4} + \frac {3177 x}{16} + \frac {3283 \log {\left (2 x - 1 \right )}}{16} - \frac {3773}{64 x - 32} \]
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Time = 0.20 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.76 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {45}{4} \, x^{3} + \frac {243}{4} \, x^{2} + \frac {3177}{16} \, x - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} + \frac {3283}{16} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.39 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {9}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {69}{2 \, x - 1} + \frac {476}{{\left (2 \, x - 1\right )}^{2}} + 5\right )} - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} - \frac {3283}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.71 \[ \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx=\frac {3177\,x}{16}+\frac {3283\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {3773}{64\,\left (x-\frac {1}{2}\right )}+\frac {243\,x^2}{4}+\frac {45\,x^3}{4} \]
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