Integrand size = 20, antiderivative size = 37 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {7 (3+5 x)^3}{12 (2+3 x)^4}+\frac {3 (3+5 x)^3}{4 (2+3 x)^3} \]
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Time = 0.00 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {79, 37} \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {3 (5 x+3)^3}{4 (3 x+2)^3}+\frac {7 (5 x+3)^3}{12 (3 x+2)^4} \]
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Rule 37
Rule 79
Rubi steps \begin{align*} \text {integral}& = \frac {7 (3+5 x)^3}{12 (2+3 x)^4}+\frac {9}{4} \int \frac {(3+5 x)^2}{(2+3 x)^4} \, dx \\ & = \frac {7 (3+5 x)^3}{12 (2+3 x)^4}+\frac {3 (3+5 x)^3}{4 (2+3 x)^3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.70 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {25+312 x+810 x^2+600 x^3}{36 (2+3 x)^4} \]
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Time = 2.17 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.68
method | result | size |
gosper | \(\frac {600 x^{3}+810 x^{2}+312 x +25}{36 \left (2+3 x \right )^{4}}\) | \(25\) |
risch | \(\frac {\frac {50}{3} x^{3}+\frac {45}{2} x^{2}+\frac {26}{3} x +\frac {25}{36}}{\left (2+3 x \right )^{4}}\) | \(25\) |
norman | \(\frac {\frac {105}{8} x^{2}+\frac {175}{24} x^{3}+\frac {9}{2} x -\frac {225}{64} x^{4}}{\left (2+3 x \right )^{4}}\) | \(28\) |
parallelrisch | \(\frac {-675 x^{4}+1400 x^{3}+2520 x^{2}+864 x}{192 \left (2+3 x \right )^{4}}\) | \(29\) |
default | \(\frac {50}{81 \left (2+3 x \right )}-\frac {65}{54 \left (2+3 x \right )^{2}}-\frac {7}{324 \left (2+3 x \right )^{4}}+\frac {8}{27 \left (2+3 x \right )^{3}}\) | \(38\) |
meijerg | \(\frac {9 x \left (\frac {27}{8} x^{3}+9 x^{2}+9 x +4\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {x^{2} \left (\frac {9}{4} x^{2}+6 x +6\right )}{32 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {35 x^{3} \left (\frac {3 x}{2}+4\right )}{384 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {25 x^{4}}{64 \left (1+\frac {3 x}{2}\right )^{4}}\) | \(78\) |
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Time = 0.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.05 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.00 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=- \frac {- 600 x^{3} - 810 x^{2} - 312 x - 25}{2916 x^{4} + 7776 x^{3} + 7776 x^{2} + 3456 x + 576} \]
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Time = 0.20 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.05 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
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Time = 0.27 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.00 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {50}{81 \, {\left (3 \, x + 2\right )}} - \frac {65}{54 \, {\left (3 \, x + 2\right )}^{2}} + \frac {8}{27 \, {\left (3 \, x + 2\right )}^{3}} - \frac {7}{324 \, {\left (3 \, x + 2\right )}^{4}} \]
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Time = 1.19 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.00 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx=\frac {50}{81\,\left (3\,x+2\right )}-\frac {65}{54\,{\left (3\,x+2\right )}^2}+\frac {8}{27\,{\left (3\,x+2\right )}^3}-\frac {7}{324\,{\left (3\,x+2\right )}^4} \]
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