Optimal. Leaf size=76 \[ \frac {27776932 x}{1953125}+\frac {17592879 x^2}{781250}-\frac {1512378 x^3}{78125}-\frac {213867 x^4}{2500}-\frac {656424 x^5}{15625}+\frac {116397 x^6}{1250}+\frac {107892 x^7}{875}+\frac {2187 x^8}{50}-\frac {121}{9765625 (3+5 x)}+\frac {2497 \log (3+5 x)}{9765625} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 76, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {2187 x^8}{50}+\frac {107892 x^7}{875}+\frac {116397 x^6}{1250}-\frac {656424 x^5}{15625}-\frac {213867 x^4}{2500}-\frac {1512378 x^3}{78125}+\frac {17592879 x^2}{781250}+\frac {27776932 x}{1953125}-\frac {121}{9765625 (5 x+3)}+\frac {2497 \log (5 x+3)}{9765625} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^2} \, dx &=\int \left (\frac {27776932}{1953125}+\frac {17592879 x}{390625}-\frac {4537134 x^2}{78125}-\frac {213867 x^3}{625}-\frac {656424 x^4}{3125}+\frac {349191 x^5}{625}+\frac {107892 x^6}{125}+\frac {8748 x^7}{25}+\frac {121}{1953125 (3+5 x)^2}+\frac {2497}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac {27776932 x}{1953125}+\frac {17592879 x^2}{781250}-\frac {1512378 x^3}{78125}-\frac {213867 x^4}{2500}-\frac {656424 x^5}{15625}+\frac {116397 x^6}{1250}+\frac {107892 x^7}{875}+\frac {2187 x^8}{50}-\frac {121}{9765625 (3+5 x)}+\frac {2497 \log (3+5 x)}{9765625}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 69, normalized size = 0.91 \begin {gather*} \frac {9997654777+74994343395 x+189581876750 x^2+74537846250 x^3-483208621875 x^4-757103878125 x^5+94742156250 x^6+1142289843750 x^7+1022308593750 x^8+299003906250 x^9+349580 (3+5 x) \log (3+5 x)}{1367187500 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 57, normalized size = 0.75
method | result | size |
risch | \(\frac {2187 x^{8}}{50}+\frac {107892 x^{7}}{875}+\frac {116397 x^{6}}{1250}-\frac {656424 x^{5}}{15625}-\frac {213867 x^{4}}{2500}-\frac {1512378 x^{3}}{78125}+\frac {17592879 x^{2}}{781250}+\frac {27776932 x}{1953125}-\frac {121}{48828125 \left (x +\frac {3}{5}\right )}+\frac {2497 \ln \left (3+5 x \right )}{9765625}\) | \(55\) |
default | \(\frac {27776932 x}{1953125}+\frac {17592879 x^{2}}{781250}-\frac {1512378 x^{3}}{78125}-\frac {213867 x^{4}}{2500}-\frac {656424 x^{5}}{15625}+\frac {116397 x^{6}}{1250}+\frac {107892 x^{7}}{875}+\frac {2187 x^{8}}{50}-\frac {121}{9765625 \left (3+5 x \right )}+\frac {2497 \ln \left (3+5 x \right )}{9765625}\) | \(57\) |
norman | \(\frac {\frac {249992509}{5859375} x +\frac {108332501}{781250} x^{2}+\frac {8518611}{156250} x^{3}-\frac {22089537}{62500} x^{4}-\frac {34610463}{62500} x^{5}+\frac {433107}{6250} x^{6}+\frac {1462131}{1750} x^{7}+\frac {261711}{350} x^{8}+\frac {2187}{10} x^{9}}{3+5 x}+\frac {2497 \ln \left (3+5 x \right )}{9765625}\) | \(62\) |
meijerg | \(-\frac {1856 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {2497 \ln \left (1+\frac {5 x}{3}\right )}{9765625}+\frac {1184 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}+\frac {2772 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}-\frac {40824 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}+\frac {22113 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}+\frac {111537 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{78125 \left (1+\frac {5 x}{3}\right )}-\frac {3483891 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{3125000 \left (1+\frac {5 x}{3}\right )}+\frac {2598156 x \left (\frac {390625}{243} x^{7}-\frac {312500}{243} x^{6}+\frac {87500}{81} x^{5}-\frac {8750}{9} x^{4}+\frac {8750}{9} x^{3}-\frac {3500}{3} x^{2}+2100 x +2520\right )}{13671875 \left (1+\frac {5 x}{3}\right )}-\frac {4782969 x \left (-\frac {13671875}{6561} x^{8}+\frac {390625}{243} x^{7}-\frac {312500}{243} x^{6}+\frac {87500}{81} x^{5}-\frac {8750}{9} x^{4}+\frac {8750}{9} x^{3}-\frac {3500}{3} x^{2}+2100 x +2520\right )}{136718750 \left (1+\frac {5 x}{3}\right )}\) | \(280\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 56, normalized size = 0.74 \begin {gather*} \frac {2187}{50} \, x^{8} + \frac {107892}{875} \, x^{7} + \frac {116397}{1250} \, x^{6} - \frac {656424}{15625} \, x^{5} - \frac {213867}{2500} \, x^{4} - \frac {1512378}{78125} \, x^{3} + \frac {17592879}{781250} \, x^{2} + \frac {27776932}{1953125} \, x - \frac {121}{9765625 \, {\left (5 \, x + 3\right )}} + \frac {2497}{9765625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 67, normalized size = 0.88 \begin {gather*} \frac {59800781250 \, x^{9} + 204461718750 \, x^{8} + 228457968750 \, x^{7} + 18948431250 \, x^{6} - 151420775625 \, x^{5} - 96641724375 \, x^{4} + 14907569250 \, x^{3} + 37916375350 \, x^{2} + 69916 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 11666311440 \, x - 3388}{273437500 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 68, normalized size = 0.89 \begin {gather*} \frac {2187 x^{8}}{50} + \frac {107892 x^{7}}{875} + \frac {116397 x^{6}}{1250} - \frac {656424 x^{5}}{15625} - \frac {213867 x^{4}}{2500} - \frac {1512378 x^{3}}{78125} + \frac {17592879 x^{2}}{781250} + \frac {27776932 x}{1953125} + \frac {2497 \log {\left (5 x + 3 \right )}}{9765625} - \frac {121}{48828125 x + 29296875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.27, size = 102, normalized size = 1.34 \begin {gather*} -\frac {1}{1367187500} \, {\left (5 \, x + 3\right )}^{8} {\left (\frac {1516320}{5 \, x + 3} - \frac {1411830}{{\left (5 \, x + 3\right )}^{2}} - \frac {11319588}{{\left (5 \, x + 3\right )}^{3}} - \frac {17377605}{{\left (5 \, x + 3\right )}^{4}} - \frac {14103180}{{\left (5 \, x + 3\right )}^{5}} - \frac {7427910}{{\left (5 \, x + 3\right )}^{6}} - \frac {3072860}{{\left (5 \, x + 3\right )}^{7}} - 153090\right )} - \frac {121}{9765625 \, {\left (5 \, x + 3\right )}} - \frac {2497}{9765625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 54, normalized size = 0.71 \begin {gather*} \frac {27776932\,x}{1953125}+\frac {2497\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {121}{48828125\,\left (x+\frac {3}{5}\right )}+\frac {17592879\,x^2}{781250}-\frac {1512378\,x^3}{78125}-\frac {213867\,x^4}{2500}-\frac {656424\,x^5}{15625}+\frac {116397\,x^6}{1250}+\frac {107892\,x^7}{875}+\frac {2187\,x^8}{50} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________