Integrand size = 22, antiderivative size = 81 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {49}{54 (2+3 x)^6}+\frac {217}{45 (2+3 x)^5}+\frac {121}{4 (2+3 x)^4}+\frac {605}{3 (2+3 x)^3}+\frac {3025}{2 (2+3 x)^2}+\frac {15125}{2+3 x}-75625 \log (2+3 x)+75625 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 81, 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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {15125}{3 x+2}+\frac {3025}{2 (3 x+2)^2}+\frac {605}{3 (3 x+2)^3}+\frac {121}{4 (3 x+2)^4}+\frac {217}{45 (3 x+2)^5}+\frac {49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{3 (2+3 x)^7}-\frac {217}{3 (2+3 x)^6}-\frac {363}{(2+3 x)^5}-\frac {1815}{(2+3 x)^4}-\frac {9075}{(2+3 x)^3}-\frac {45375}{(2+3 x)^2}-\frac {226875}{2+3 x}+\frac {378125}{3+5 x}\right ) \, dx \\ & = \frac {49}{54 (2+3 x)^6}+\frac {217}{45 (2+3 x)^5}+\frac {121}{4 (2+3 x)^4}+\frac {605}{3 (2+3 x)^3}+\frac {3025}{2 (2+3 x)^2}+\frac {15125}{2+3 x}-75625 \log (2+3 x)+75625 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.68 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {275370238+2042732232 x+6063045615 x^2+9000258300 x^3+6681831750 x^4+1984702500 x^5}{540 (2+3 x)^6}-75625 \log (5 (2+3 x))+75625 \log (3+5 x) \]
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Time = 2.34 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.63
method | result | size |
norman | \(\frac {3675375 x^{5}+16667145 x^{3}+\frac {24747525}{2} x^{4}+\frac {44911449}{4} x^{2}+\frac {56742562}{15} x +\frac {137685119}{270}}{\left (2+3 x \right )^{6}}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(51\) |
risch | \(\frac {3675375 x^{5}+16667145 x^{3}+\frac {24747525}{2} x^{4}+\frac {44911449}{4} x^{2}+\frac {56742562}{15} x +\frac {137685119}{270}}{\left (2+3 x \right )^{6}}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(52\) |
default | \(\frac {49}{54 \left (2+3 x \right )^{6}}+\frac {217}{45 \left (2+3 x \right )^{5}}+\frac {121}{4 \left (2+3 x \right )^{4}}+\frac {605}{3 \left (2+3 x \right )^{3}}+\frac {3025}{2 \left (2+3 x \right )^{2}}+\frac {15125}{2+3 x}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(72\) |
parallelrisch | \(-\frac {516266560 x -104544000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+209088000000 \ln \left (\frac {2}{3}+x \right ) x^{3}-27878400000 \ln \left (x +\frac {3}{5}\right ) x +104544000000 \ln \left (\frac {2}{3}+x \right ) x^{2}+27878400000 \ln \left (\frac {2}{3}+x \right ) x +12517752852 x^{5}+3717498213 x^{6}+11362646240 x^{3}+16864113420 x^{4}+3828977680 x^{2}+235224000000 \ln \left (\frac {2}{3}+x \right ) x^{4}+3097600000 \ln \left (\frac {2}{3}+x \right )-3097600000 \ln \left (x +\frac {3}{5}\right )+141134400000 \ln \left (\frac {2}{3}+x \right ) x^{5}-209088000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-141134400000 \ln \left (x +\frac {3}{5}\right ) x^{5}-235224000000 \ln \left (x +\frac {3}{5}\right ) x^{4}+35283600000 \ln \left (\frac {2}{3}+x \right ) x^{6}-35283600000 \ln \left (x +\frac {3}{5}\right ) x^{6}}{640 \left (2+3 x \right )^{6}}\) | \(155\) |
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Time = 0.22 (sec) , antiderivative size = 135, normalized size of antiderivative = 1.67 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 40837500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 40837500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 2042732232 \, x + 275370238}{540 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {1984702500 x^{5} + 6681831750 x^{4} + 9000258300 x^{3} + 6063045615 x^{2} + 2042732232 x + 275370238}{393660 x^{6} + 1574640 x^{5} + 2624400 x^{4} + 2332800 x^{3} + 1166400 x^{2} + 311040 x + 34560} + 75625 \log {\left (x + \frac {3}{5} \right )} - 75625 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.20 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 75625 \, \log \left (5 \, x + 3\right ) - 75625 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.65 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \, {\left (3 \, x + 2\right )}^{6}} + 75625 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 75625 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.33 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx=\frac {\frac {15125\,x^5}{3}+\frac {305525\,x^4}{18}+\frac {1851905\,x^3}{81}+\frac {1663387\,x^2}{108}+\frac {56742562\,x}{10935}+\frac {137685119}{196830}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}}-151250\,\mathrm {atanh}\left (30\,x+19\right ) \]
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