Optimal. Leaf size=59 \[ \frac {290521}{256 (1-2 x)^2}-\frac {381073}{64 (1-2 x)}-\frac {176055 x}{32}-\frac {54783 x^2}{32}-\frac {7245 x^3}{16}-\frac {2025 x^4}{32}-\frac {832951}{128} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 59, 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 {2025 x^4}{32}-\frac {7245 x^3}{16}-\frac {54783 x^2}{32}-\frac {176055 x}{32}-\frac {381073}{64 (1-2 x)}+\frac {290521}{256 (1-2 x)^2}-\frac {832951}{128} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {176055}{32}-\frac {54783 x}{16}-\frac {21735 x^2}{16}-\frac {2025 x^3}{8}-\frac {290521}{64 (-1+2 x)^3}-\frac {381073}{32 (-1+2 x)^2}-\frac {832951}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {290521}{256 (1-2 x)^2}-\frac {381073}{64 (1-2 x)}-\frac {176055 x}{32}-\frac {54783 x^2}{32}-\frac {7245 x^3}{16}-\frac {2025 x^4}{32}-\frac {832951}{128} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 56, normalized size = 0.95 \begin {gather*} -\frac {808965+3354020 x-17025300 x^2+7993248 x^3+2611152 x^4+797760 x^5+129600 x^6+3331804 (1-2 x)^2 \log (1-2 x)}{512 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 46, normalized size = 0.78
method | result | size |
risch | \(-\frac {2025 x^{4}}{32}-\frac {7245 x^{3}}{16}-\frac {54783 x^{2}}{32}-\frac {176055 x}{32}+\frac {\frac {381073 x}{32}-\frac {1233771}{256}}{\left (-1+2 x \right )^{2}}-\frac {832951 \ln \left (-1+2 x \right )}{128}\) | \(42\) |
default | \(-\frac {2025 x^{4}}{32}-\frac {7245 x^{3}}{16}-\frac {54783 x^{2}}{32}-\frac {176055 x}{32}+\frac {381073}{64 \left (-1+2 x \right )}+\frac {290521}{256 \left (-1+2 x \right )^{2}}-\frac {832951 \ln \left (-1+2 x \right )}{128}\) | \(46\) |
norman | \(\frac {-\frac {823735}{64} x +\frac {2532645}{64} x^{2}-\frac {249789}{16} x^{3}-\frac {163197}{32} x^{4}-\frac {12465}{8} x^{5}-\frac {2025}{8} x^{6}}{\left (-1+2 x \right )^{2}}-\frac {832951 \ln \left (-1+2 x \right )}{128}\) | \(47\) |
meijerg | \(\frac {72 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {672 x^{2}}{\left (1-2 x \right )^{2}}-\frac {653 x \left (-18 x +6\right )}{3 \left (1-2 x \right )^{2}}-\frac {832951 \ln \left (1-2 x \right )}{128}-\frac {1353 x \left (16 x^{2}-36 x +12\right )}{4 \left (1-2 x \right )^{2}}-\frac {12609 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{160 \left (1-2 x \right )^{2}}-\frac {1305 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{32 \left (1-2 x \right )^{2}}-\frac {2025 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{1792 \left (1-2 x \right )^{2}}\) | \(162\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 46, normalized size = 0.78 \begin {gather*} -\frac {2025}{32} \, x^{4} - \frac {7245}{16} \, x^{3} - \frac {54783}{32} \, x^{2} - \frac {176055}{32} \, x + \frac {3773 \, {\left (808 \, x - 327\right )}}{256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {832951}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 62, normalized size = 1.05 \begin {gather*} -\frac {64800 \, x^{6} + 398880 \, x^{5} + 1305576 \, x^{4} + 3996624 \, x^{3} - 5195496 \, x^{2} + 1665902 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1640144 \, x + 1233771}{256 \, {\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 = 0.05, size = 51, normalized size = 0.86 \begin {gather*} - \frac {2025 x^{4}}{32} - \frac {7245 x^{3}}{16} - \frac {54783 x^{2}}{32} - \frac {176055 x}{32} - \frac {1233771 - 3048584 x}{1024 x^{2} - 1024 x + 256} - \frac {832951 \log {\left (2 x - 1 \right )}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.52, size = 42, normalized size = 0.71 \begin {gather*} -\frac {2025}{32} \, x^{4} - \frac {7245}{16} \, x^{3} - \frac {54783}{32} \, x^{2} - \frac {176055}{32} \, x + \frac {3773 \, {\left (808 \, x - 327\right )}}{256 \, {\left (2 \, x - 1\right )}^{2}} - \frac {832951}{128} \, \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 = 0.03, size = 41, normalized size = 0.69 \begin {gather*} \frac {\frac {381073\,x}{128}-\frac {1233771}{1024}}{x^2-x+\frac {1}{4}}-\frac {832951\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {176055\,x}{32}-\frac {54783\,x^2}{32}-\frac {7245\,x^3}{16}-\frac {2025\,x^4}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________