Optimal. Leaf size=62 \[ \frac {2033647}{256 (1-2 x)}+\frac {2104901 x}{64}+\frac {2412699 x^2}{128}+\frac {89913 x^3}{8}+\frac {342333 x^4}{64}+\frac {6723 x^5}{4}+\frac {2025 x^6}{8}+\frac {6206585}{256} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 62, 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^6}{8}+\frac {6723 x^5}{4}+\frac {342333 x^4}{64}+\frac {89913 x^3}{8}+\frac {2412699 x^2}{128}+\frac {2104901 x}{64}+\frac {2033647}{256 (1-2 x)}+\frac {6206585}{256} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {2104901}{64}+\frac {2412699 x}{64}+\frac {269739 x^2}{8}+\frac {342333 x^3}{16}+\frac {33615 x^4}{4}+\frac {6075 x^5}{4}+\frac {2033647}{128 (-1+2 x)^2}+\frac {6206585}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {2033647}{256 (1-2 x)}+\frac {2104901 x}{64}+\frac {2412699 x^2}{128}+\frac {89913 x^3}{8}+\frac {342333 x^4}{64}+\frac {6723 x^5}{4}+\frac {2025 x^6}{8}+\frac {6206585}{256} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 59, normalized size = 0.95 \begin {gather*} \frac {15368793-80685178 x+48055240 x^2+27094320 x^3+17540400 x^4+9233568 x^5+3182976 x^6+518400 x^7+24826340 (-1+2 x) \log (1-2 x)}{1024 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 47, normalized size = 0.76
method | result | size |
risch | \(\frac {2025 x^{6}}{8}+\frac {6723 x^{5}}{4}+\frac {342333 x^{4}}{64}+\frac {89913 x^{3}}{8}+\frac {2412699 x^{2}}{128}+\frac {2104901 x}{64}-\frac {2033647}{512 \left (-\frac {1}{2}+x \right )}+\frac {6206585 \ln \left (-1+2 x \right )}{256}\) | \(45\) |
default | \(\frac {2025 x^{6}}{8}+\frac {6723 x^{5}}{4}+\frac {342333 x^{4}}{64}+\frac {89913 x^{3}}{8}+\frac {2412699 x^{2}}{128}+\frac {2104901 x}{64}-\frac {2033647}{256 \left (-1+2 x \right )}+\frac {6206585 \ln \left (-1+2 x \right )}{256}\) | \(47\) |
norman | \(\frac {-\frac {6243449}{128} x +\frac {6006905}{128} x^{2}+\frac {1693395}{64} x^{3}+\frac {1096275}{64} x^{4}+\frac {288549}{32} x^{5}+\frac {24867}{8} x^{6}+\frac {2025}{4} x^{7}}{-1+2 x}+\frac {6206585 \ln \left (-1+2 x \right )}{256}\) | \(52\) |
meijerg | \(\frac {1848 x}{1-2 x}+\frac {6206585 \ln \left (1-2 x \right )}{256}+\frac {3620 x \left (-6 x +6\right )}{3 \left (1-2 x \right )}+\frac {4665 x \left (-8 x^{2}-12 x +12\right )}{4 \left (1-2 x \right )}+\frac {1923 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{8 \left (1-2 x \right )}+\frac {17829 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{128 \left (1-2 x \right )}+\frac {1377 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{224 \left (1-2 x \right )}+\frac {405 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{1024 \left (1-2 x \right )}\) | \(185\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.33, size = 46, normalized size = 0.74 \begin {gather*} \frac {2025}{8} \, x^{6} + \frac {6723}{4} \, x^{5} + \frac {342333}{64} \, x^{4} + \frac {89913}{8} \, x^{3} + \frac {2412699}{128} \, x^{2} + \frac {2104901}{64} \, x - \frac {2033647}{256 \, {\left (2 \, x - 1\right )}} + \frac {6206585}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.79, size = 57, normalized size = 0.92 \begin {gather*} \frac {129600 \, x^{7} + 795744 \, x^{6} + 2308392 \, x^{5} + 4385100 \, x^{4} + 6773580 \, x^{3} + 12013810 \, x^{2} + 6206585 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 8419604 \, x - 2033647}{256 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 54, normalized size = 0.87 \begin {gather*} \frac {2025 x^{6}}{8} + \frac {6723 x^{5}}{4} + \frac {342333 x^{4}}{64} + \frac {89913 x^{3}}{8} + \frac {2412699 x^{2}}{128} + \frac {2104901 x}{64} + \frac {6206585 \log {\left (2 x - 1 \right )}}{256} - \frac {2033647}{512 x - 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.27, size = 84, normalized size = 1.35 \begin {gather*} \frac {1}{1024} \, {\left (2 \, x - 1\right )}^{6} {\left (\frac {78084}{2 \, x - 1} + \frac {672003}{{\left (2 \, x - 1\right )}^{2}} + \frac {3426780}{{\left (2 \, x - 1\right )}^{3}} + \frac {11793810}{{\left (2 \, x - 1\right )}^{4}} + \frac {32468380}{{\left (2 \, x - 1\right )}^{5}} + 4050\right )} - \frac {2033647}{256 \, {\left (2 \, x - 1\right )}} - \frac {6206585}{256} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 44, normalized size = 0.71 \begin {gather*} \frac {2104901\,x}{64}+\frac {6206585\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {2033647}{512\,\left (x-\frac {1}{2}\right )}+\frac {2412699\,x^2}{128}+\frac {89913\,x^3}{8}+\frac {342333\,x^4}{64}+\frac {6723\,x^5}{4}+\frac {2025\,x^6}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________