Integrand size = 22, antiderivative size = 58 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=\frac {416223 x}{78125}-\frac {138741 x^2}{31250}-\frac {128753 x^3}{9375}+\frac {31251 x^4}{2500}+\frac {14958 x^5}{625}-\frac {306 x^6}{25}-\frac {648 x^7}{35}+\frac {1331 \log (3+5 x)}{390625} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 58, 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} \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=-\frac {648 x^7}{35}-\frac {306 x^6}{25}+\frac {14958 x^5}{625}+\frac {31251 x^4}{2500}-\frac {128753 x^3}{9375}-\frac {138741 x^2}{31250}+\frac {416223 x}{78125}+\frac {1331 \log (5 x+3)}{390625} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {416223}{78125}-\frac {138741 x}{15625}-\frac {128753 x^2}{3125}+\frac {31251 x^3}{625}+\frac {14958 x^4}{125}-\frac {1836 x^5}{25}-\frac {648 x^6}{5}+\frac {1331}{78125 (3+5 x)}\right ) \, dx \\ & = \frac {416223 x}{78125}-\frac {138741 x^2}{31250}-\frac {128753 x^3}{9375}+\frac {31251 x^4}{2500}+\frac {14958 x^5}{625}-\frac {306 x^6}{25}-\frac {648 x^7}{35}+\frac {1331 \log (3+5 x)}{390625} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=\frac {348168591+874068300 x-728390250 x^2-2253177500 x^3+2050846875 x^4+3926475000 x^5-2008125000 x^6-3037500000 x^7+559020 \log (3+5 x)}{164062500} \]
[In]
[Out]
Time = 0.80 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {648 x^{7}}{35}-\frac {306 x^{6}}{25}+\frac {14958 x^{5}}{625}+\frac {31251 x^{4}}{2500}-\frac {128753 x^{3}}{9375}-\frac {138741 x^{2}}{31250}+\frac {416223 x}{78125}+\frac {1331 \ln \left (x +\frac {3}{5}\right )}{390625}\) | \(41\) |
default | \(\frac {416223 x}{78125}-\frac {138741 x^{2}}{31250}-\frac {128753 x^{3}}{9375}+\frac {31251 x^{4}}{2500}+\frac {14958 x^{5}}{625}-\frac {306 x^{6}}{25}-\frac {648 x^{7}}{35}+\frac {1331 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
norman | \(\frac {416223 x}{78125}-\frac {138741 x^{2}}{31250}-\frac {128753 x^{3}}{9375}+\frac {31251 x^{4}}{2500}+\frac {14958 x^{5}}{625}-\frac {306 x^{6}}{25}-\frac {648 x^{7}}{35}+\frac {1331 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
risch | \(\frac {416223 x}{78125}-\frac {138741 x^{2}}{31250}-\frac {128753 x^{3}}{9375}+\frac {31251 x^{4}}{2500}+\frac {14958 x^{5}}{625}-\frac {306 x^{6}}{25}-\frac {648 x^{7}}{35}+\frac {1331 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {84 x \left (-5 x +6\right )}{25}-\frac {42 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}-\frac {5481 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{12500}+\frac {5103 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{31250}+\frac {2187 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{78125}-\frac {19683 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{2734375}\) | \(133\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=-\frac {648}{35} \, x^{7} - \frac {306}{25} \, x^{6} + \frac {14958}{625} \, x^{5} + \frac {31251}{2500} \, x^{4} - \frac {128753}{9375} \, x^{3} - \frac {138741}{31250} \, x^{2} + \frac {416223}{78125} \, x + \frac {1331}{390625} \, \log \left (5 \, x + 3\right ) \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=- \frac {648 x^{7}}{35} - \frac {306 x^{6}}{25} + \frac {14958 x^{5}}{625} + \frac {31251 x^{4}}{2500} - \frac {128753 x^{3}}{9375} - \frac {138741 x^{2}}{31250} + \frac {416223 x}{78125} + \frac {1331 \log {\left (5 x + 3 \right )}}{390625} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=-\frac {648}{35} \, x^{7} - \frac {306}{25} \, x^{6} + \frac {14958}{625} \, x^{5} + \frac {31251}{2500} \, x^{4} - \frac {128753}{9375} \, x^{3} - \frac {138741}{31250} \, x^{2} + \frac {416223}{78125} \, x + \frac {1331}{390625} \, \log \left (5 \, x + 3\right ) \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=-\frac {648}{35} \, x^{7} - \frac {306}{25} \, x^{6} + \frac {14958}{625} \, x^{5} + \frac {31251}{2500} \, x^{4} - \frac {128753}{9375} \, x^{3} - \frac {138741}{31250} \, x^{2} + \frac {416223}{78125} \, x + \frac {1331}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx=\frac {416223\,x}{78125}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {138741\,x^2}{31250}-\frac {128753\,x^3}{9375}+\frac {31251\,x^4}{2500}+\frac {14958\,x^5}{625}-\frac {306\,x^6}{25}-\frac {648\,x^7}{35} \]
[In]
[Out]