Integrand size = 22, antiderivative size = 72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {83333293 x}{1953125}+\frac {80555569 x^2}{781250}+\frac {1327159 x^3}{78125}-\frac {20577159 x^4}{62500}-\frac {7315947 x^5}{15625}+\frac {130383 x^6}{1250}+\frac {672867 x^7}{875}+\frac {16767 x^8}{25}+\frac {972 x^9}{5}+\frac {121 \log (3+5 x)}{9765625} \]
83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-20577159/62500*x^ 4-7315947/15625*x^5+130383/1250*x^6+672867/875*x^7+16767/25*x^8+972/5*x^9+ 121/9765625*ln(3+5*x)
Time = 0.01 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {7880238537+58333305100 x+140972245750 x^2+23225282500 x^3-450125353125 x^4-640145362500 x^5+142606406250 x^6+1051354687500 x^7+916945312500 x^8+265781250000 x^9+16940 \log (3+5 x)}{1367187500} \]
(7880238537 + 58333305100*x + 140972245750*x^2 + 23225282500*x^3 - 4501253 53125*x^4 - 640145362500*x^5 + 142606406250*x^6 + 1051354687500*x^7 + 9169 45312500*x^8 + 265781250000*x^9 + 16940*Log[3 + 5*x])/1367187500
Time = 0.19 (sec) , antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {99, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {(1-2 x)^2 (3 x+2)^7}{5 x+3} \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (\frac {8748 x^8}{5}+\frac {134136 x^7}{25}+\frac {672867 x^6}{125}+\frac {391149 x^5}{625}-\frac {7315947 x^4}{3125}-\frac {20577159 x^3}{15625}+\frac {3981477 x^2}{78125}+\frac {80555569 x}{390625}+\frac {121}{1953125 (5 x+3)}+\frac {83333293}{1953125}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {972 x^9}{5}+\frac {16767 x^8}{25}+\frac {672867 x^7}{875}+\frac {130383 x^6}{1250}-\frac {7315947 x^5}{15625}-\frac {20577159 x^4}{62500}+\frac {1327159 x^3}{78125}+\frac {80555569 x^2}{781250}+\frac {83333293 x}{1953125}+\frac {121 \log (5 x+3)}{9765625}\) |
(83333293*x)/1953125 + (80555569*x^2)/781250 + (1327159*x^3)/78125 - (2057 7159*x^4)/62500 - (7315947*x^5)/15625 + (130383*x^6)/1250 + (672867*x^7)/8 75 + (16767*x^8)/25 + (972*x^9)/5 + (121*Log[3 + 5*x])/9765625
3.13.89.3.1 Defintions of rubi rules used
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] && (IntegerQ[p] | | (GtQ[m, 0] && GeQ[n, -1]))
Time = 2.35 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(\frac {972 x^{9}}{5}+\frac {16767 x^{8}}{25}+\frac {672867 x^{7}}{875}+\frac {130383 x^{6}}{1250}-\frac {7315947 x^{5}}{15625}-\frac {20577159 x^{4}}{62500}+\frac {1327159 x^{3}}{78125}+\frac {80555569 x^{2}}{781250}+\frac {83333293 x}{1953125}+\frac {121 \ln \left (x +\frac {3}{5}\right )}{9765625}\) | \(51\) |
default | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
norman | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
risch | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{9765625}+\frac {832 x}{5}-\frac {592 x \left (-5 x +6\right )}{25}-\frac {2772 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}+\frac {30618 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}-\frac {66339 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}-\frac {111537 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{156250}+\frac {10451673 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{21875000}-\frac {1948617 x \left (-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{27343750}+\frac {1594323 x \left (\frac {109375000}{6561} x^{8}-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{136718750}\) | \(217\) |
972/5*x^9+16767/25*x^8+672867/875*x^7+130383/1250*x^6-7315947/15625*x^5-20 577159/62500*x^4+1327159/78125*x^3+80555569/781250*x^2+83333293/1953125*x+ 121/9765625*ln(x+3/5)
Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left (5 \, x + 3\right ) \]
972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/1562 5*x^5 - 20577159/62500*x^4 + 1327159/78125*x^3 + 80555569/781250*x^2 + 833 33293/1953125*x + 121/9765625*log(5*x + 3)
Time = 0.05 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972 x^{9}}{5} + \frac {16767 x^{8}}{25} + \frac {672867 x^{7}}{875} + \frac {130383 x^{6}}{1250} - \frac {7315947 x^{5}}{15625} - \frac {20577159 x^{4}}{62500} + \frac {1327159 x^{3}}{78125} + \frac {80555569 x^{2}}{781250} + \frac {83333293 x}{1953125} + \frac {121 \log {\left (5 x + 3 \right )}}{9765625} \]
972*x**9/5 + 16767*x**8/25 + 672867*x**7/875 + 130383*x**6/1250 - 7315947* x**5/15625 - 20577159*x**4/62500 + 1327159*x**3/78125 + 80555569*x**2/7812 50 + 83333293*x/1953125 + 121*log(5*x + 3)/9765625
Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left (5 \, x + 3\right ) \]
972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/1562 5*x^5 - 20577159/62500*x^4 + 1327159/78125*x^3 + 80555569/781250*x^2 + 833 33293/1953125*x + 121/9765625*log(5*x + 3)
Time = 0.28 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/1562 5*x^5 - 20577159/62500*x^4 + 1327159/78125*x^3 + 80555569/781250*x^2 + 833 33293/1953125*x + 121/9765625*log(abs(5*x + 3))
Time = 0.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {83333293\,x}{1953125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{9765625}+\frac {80555569\,x^2}{781250}+\frac {1327159\,x^3}{78125}-\frac {20577159\,x^4}{62500}-\frac {7315947\,x^5}{15625}+\frac {130383\,x^6}{1250}+\frac {672867\,x^7}{875}+\frac {16767\,x^8}{25}+\frac {972\,x^9}{5} \]