Integrand size = 22, antiderivative size = 57 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (2+3 x)+6934 \log (3+5 x) \]
[Out]
Time = 0.03 (sec) , antiderivative size = 57, 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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {707}{3 x+2}+\frac {1133}{5 x+3}+\frac {49}{2 (3 x+2)^2}-\frac {121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3) \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {147}{(2+3 x)^3}-\frac {2121}{(2+3 x)^2}-\frac {20802}{2+3 x}+\frac {605}{(3+5 x)^3}-\frac {5665}{(3+5 x)^2}+\frac {34670}{3+5 x}\right ) \, dx \\ & = \frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (2+3 x)+6934 \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.04 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (5 (2+3 x))+6934 \log (3+5 x) \]
[In]
[Out]
Time = 2.37 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84
method | result | size |
norman | \(\frac {104010 x^{3}+124966 x +197619 x^{2}+\frac {52601}{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(48\) |
risch | \(\frac {104010 x^{3}+124966 x +197619 x^{2}+\frac {52601}{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(49\) |
default | \(\frac {49}{2 \left (2+3 x \right )^{2}}+\frac {707}{2+3 x}-\frac {121}{2 \left (3+5 x \right )^{2}}+\frac {1133}{3+5 x}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(54\) |
parallelrisch | \(-\frac {112330800 \ln \left (\frac {2}{3}+x \right ) x^{4}-112330800 \ln \left (x +\frac {3}{5}\right ) x^{4}+284571360 \ln \left (\frac {2}{3}+x \right ) x^{3}-284571360 \ln \left (x +\frac {3}{5}\right ) x^{3}+11835225 x^{4}+270093168 \ln \left (\frac {2}{3}+x \right ) x^{2}-270093168 \ln \left (x +\frac {3}{5}\right ) x^{2}+22493850 x^{3}+113828544 \ln \left (\frac {2}{3}+x \right ) x -113828544 \ln \left (x +\frac {3}{5}\right ) x +14228573 x^{2}+17972928 \ln \left (\frac {2}{3}+x \right )-17972928 \ln \left (x +\frac {3}{5}\right )+2995476 x}{72 \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}\) | \(116\) |
[In]
[Out]
none
Time = 0.23 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.67 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {208020 \, x^{3} + 395238 \, x^{2} + 13868 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 13868 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 249932 \, x + 52601}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.89 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {208020 x^{3} + 395238 x^{2} + 249932 x + 52601}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 6934 \log {\left (x + \frac {3}{5} \right )} - 6934 \log {\left (x + \frac {2}{3} \right )} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 6934 \, \log \left (5 \, x + 3\right ) - 6934 \, \log \left (3 \, x + 2\right ) \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 6934 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6934 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {\frac {6934\,x^3}{15}+\frac {65873\,x^2}{75}+\frac {124966\,x}{225}+\frac {52601}{450}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}}-13868\,\mathrm {atanh}\left (30\,x+19\right ) \]
[In]
[Out]