Optimal. Leaf size=80 \[ \frac {63412811}{2048 (1-2 x)^2}-\frac {246239357}{1024 (1-2 x)}-\frac {120864213 x}{256}-\frac {118841283 x^2}{512}-\frac {16042509 x^3}{128}-\frac {7568235 x^4}{128}-\frac {213597 x^5}{10}-\frac {162567 x^6}{32}-\frac {32805 x^7}{56}-\frac {106237047}{256} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {32805 x^7}{56}-\frac {162567 x^6}{32}-\frac {213597 x^5}{10}-\frac {7568235 x^4}{128}-\frac {16042509 x^3}{128}-\frac {118841283 x^2}{512}-\frac {120864213 x}{256}-\frac {246239357}{1024 (1-2 x)}+\frac {63412811}{2048 (1-2 x)^2}-\frac {106237047}{256} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac {120864213}{256}-\frac {118841283 x}{256}-\frac {48127527 x^2}{128}-\frac {7568235 x^3}{32}-\frac {213597 x^4}{2}-\frac {487701 x^5}{16}-\frac {32805 x^6}{8}-\frac {63412811}{512 (-1+2 x)^3}-\frac {246239357}{512 (-1+2 x)^2}-\frac {106237047}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {63412811}{2048 (1-2 x)^2}-\frac {246239357}{1024 (1-2 x)}-\frac {120864213 x}{256}-\frac {118841283 x^2}{512}-\frac {16042509 x^3}{128}-\frac {7568235 x^4}{128}-\frac {213597 x^5}{10}-\frac {162567 x^6}{32}-\frac {32805 x^7}{56}-\frac {106237047}{256} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 71, normalized size = 0.89 \begin {gather*} -\frac {-3752427799+44728559236 x-104409393876 x^2+38900302560 x^3+17427054960 x^4+10256718528 x^5+5596371648 x^6+2354821632 x^7+644319360 x^8+83980800 x^9+14873186580 (1-2 x)^2 \log (1-2 x)}{35840 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 61, normalized size = 0.76
method | result | size |
risch | \(-\frac {32805 x^{7}}{56}-\frac {162567 x^{6}}{32}-\frac {213597 x^{5}}{10}-\frac {7568235 x^{4}}{128}-\frac {16042509 x^{3}}{128}-\frac {118841283 x^{2}}{512}-\frac {120864213 x}{256}+\frac {\frac {246239357 x}{512}-\frac {429065903}{2048}}{\left (-1+2 x \right )^{2}}-\frac {106237047 \ln \left (-1+2 x \right )}{256}\) | \(57\) |
default | \(-\frac {32805 x^{7}}{56}-\frac {162567 x^{6}}{32}-\frac {213597 x^{5}}{10}-\frac {7568235 x^{4}}{128}-\frac {16042509 x^{3}}{128}-\frac {118841283 x^{2}}{512}-\frac {120864213 x}{256}+\frac {246239357}{1024 \left (-1+2 x \right )}+\frac {63412811}{2048 \left (-1+2 x \right )^{2}}-\frac {106237047 \ln \left (-1+2 x \right )}{256}\) | \(61\) |
norman | \(\frac {-\frac {106138743}{128} x +\frac {319284581}{128} x^{2}-\frac {34732413}{32} x^{3}-\frac {31119741}{64} x^{4}-\frac {22894461}{80} x^{5}-\frac {12491901}{80} x^{6}-\frac {4599261}{70} x^{7}-\frac {1006749}{56} x^{8}-\frac {32805}{14} x^{9}}{\left (-1+2 x \right )^{2}}-\frac {106237047 \ln \left (-1+2 x \right )}{256}\) | \(62\) |
meijerg | \(\frac {384 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {5248 x^{2}}{\left (1-2 x \right )^{2}}-\frac {8019 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{80 \left (1-2 x \right )^{2}}-\frac {106237047 \ln \left (1-2 x \right )}{256}-\frac {21627 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{2560 \left (1-2 x \right )^{2}}-\frac {6561 x \left (2560 x^{8}+1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{7168 \left (1-2 x \right )^{2}}-\frac {3213 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{\left (1-2 x \right )^{2}}-\frac {8127 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{2 \left (1-2 x \right )^{2}}-\frac {7047 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{16 \left (1-2 x \right )^{2}}-\frac {2656 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}-\frac {7056 x \left (16 x^{2}-36 x +12\right )}{\left (1-2 x \right )^{2}}\) | \(297\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.39, size = 61, normalized size = 0.76 \begin {gather*} -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {106237047}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 77, normalized size = 0.96 \begin {gather*} -\frac {167961600 \, x^{9} + 1288638720 \, x^{8} + 4709643264 \, x^{7} + 11192743296 \, x^{6} + 20513437056 \, x^{5} + 34854109920 \, x^{4} + 77800605120 \, x^{3} - 118730138940 \, x^{2} + 29746373160 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 631530340 \, x + 15017306605}{71680 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 71, normalized size = 0.89 \begin {gather*} - \frac {32805 x^{7}}{56} - \frac {162567 x^{6}}{32} - \frac {213597 x^{5}}{10} - \frac {7568235 x^{4}}{128} - \frac {16042509 x^{3}}{128} - \frac {118841283 x^{2}}{512} - \frac {120864213 x}{256} - \frac {429065903 - 984957428 x}{8192 x^{2} - 8192 x + 2048} - \frac {106237047 \log {\left (2 x - 1 \right )}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.51, size = 57, normalized size = 0.71 \begin {gather*} -\frac {32805}{56} \, x^{7} - \frac {162567}{32} \, x^{6} - \frac {213597}{10} \, x^{5} - \frac {7568235}{128} \, x^{4} - \frac {16042509}{128} \, x^{3} - \frac {118841283}{512} \, x^{2} - \frac {120864213}{256} \, x + \frac {823543 \, {\left (1196 \, x - 521\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {106237047}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 56, normalized size = 0.70 \begin {gather*} \frac {\frac {246239357\,x}{2048}-\frac {429065903}{8192}}{x^2-x+\frac {1}{4}}-\frac {106237047\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {120864213\,x}{256}-\frac {118841283\,x^2}{512}-\frac {16042509\,x^3}{128}-\frac {7568235\,x^4}{128}-\frac {213597\,x^5}{10}-\frac {162567\,x^6}{32}-\frac {32805\,x^7}{56} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________