Optimal. Leaf size=55 \[ \frac {184877}{128 (1-2 x)}+\frac {301467 x}{64}+\frac {75447 x^2}{32}+\frac {18027 x^3}{16}+\frac {2997 x^4}{8}+\frac {243 x^5}{4}+\frac {60025}{16} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 55, 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 {243 x^5}{4}+\frac {2997 x^4}{8}+\frac {18027 x^3}{16}+\frac {75447 x^2}{32}+\frac {301467 x}{64}+\frac {184877}{128 (1-2 x)}+\frac {60025}{16} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac {301467}{64}+\frac {75447 x}{16}+\frac {54081 x^2}{16}+\frac {2997 x^3}{2}+\frac {1215 x^4}{4}+\frac {184877}{64 (-1+2 x)^2}+\frac {60025}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {184877}{128 (1-2 x)}+\frac {301467 x}{64}+\frac {75447 x^2}{32}+\frac {18027 x^3}{16}+\frac {2997 x^4}{8}+\frac {243 x^5}{4}+\frac {60025}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 51, normalized size = 0.93 \begin {gather*} \frac {26663-174912 x+113010 x^2+57420 x^3+30060 x^4+11016 x^5+1944 x^6+60025 (-1+2 x) \log (1-2 x)}{-16+32 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 42, normalized size = 0.76
method | result | size |
risch | \(\frac {243 x^{5}}{4}+\frac {2997 x^{4}}{8}+\frac {18027 x^{3}}{16}+\frac {75447 x^{2}}{32}+\frac {301467 x}{64}-\frac {184877}{256 \left (-\frac {1}{2}+x \right )}+\frac {60025 \ln \left (-1+2 x \right )}{16}\) | \(40\) |
default | \(\frac {243 x^{5}}{4}+\frac {2997 x^{4}}{8}+\frac {18027 x^{3}}{16}+\frac {75447 x^{2}}{32}+\frac {301467 x}{64}-\frac {184877}{128 \left (-1+2 x \right )}+\frac {60025 \ln \left (-1+2 x \right )}{16}\) | \(42\) |
norman | \(\frac {-\frac {60793}{8} x +\frac {56505}{8} x^{2}+\frac {14355}{4} x^{3}+\frac {7515}{4} x^{4}+\frac {1377}{2} x^{5}+\frac {243}{2} x^{6}}{-1+2 x}+\frac {60025 \ln \left (-1+2 x \right )}{16}\) | \(47\) |
meijerg | \(\frac {536 x}{1-2 x}+\frac {60025 \ln \left (1-2 x \right )}{16}+\frac {280 x \left (-6 x +6\right )}{1-2 x}+\frac {855 x \left (-8 x^{2}-12 x +12\right )}{4 \left (1-2 x \right )}+\frac {261 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{8 \left (1-2 x \right )}+\frac {1593 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{128 \left (1-2 x \right )}+\frac {243 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{896 \left (1-2 x \right )}\) | \(145\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 41, normalized size = 0.75 \begin {gather*} \frac {243}{4} \, x^{5} + \frac {2997}{8} \, x^{4} + \frac {18027}{16} \, x^{3} + \frac {75447}{32} \, x^{2} + \frac {301467}{64} \, x - \frac {184877}{128 \, {\left (2 \, x - 1\right )}} + \frac {60025}{16} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.47, size = 52, normalized size = 0.95 \begin {gather*} \frac {15552 \, x^{6} + 88128 \, x^{5} + 240480 \, x^{4} + 459360 \, x^{3} + 904080 \, x^{2} + 480200 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 602934 \, x - 184877}{128 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 48, normalized size = 0.87 \begin {gather*} \frac {243 x^{5}}{4} + \frac {2997 x^{4}}{8} + \frac {18027 x^{3}}{16} + \frac {75447 x^{2}}{32} + \frac {301467 x}{64} + \frac {60025 \log {\left (2 x - 1 \right )}}{16} - \frac {184877}{256 x - 128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 75, normalized size = 1.36 \begin {gather*} \frac {3}{128} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {1404}{2 \, x - 1} + \frac {10815}{{\left (2 \, x - 1\right )}^{2}} + \frac {49980}{{\left (2 \, x - 1\right )}^{3}} + \frac {173215}{{\left (2 \, x - 1\right )}^{4}} + 81\right )} - \frac {184877}{128 \, {\left (2 \, x - 1\right )}} - \frac {60025}{16} \, \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.
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Mupad [B]
time = 0.03, size = 39, normalized size = 0.71 \begin {gather*} \frac {301467\,x}{64}+\frac {60025\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {184877}{256\,\left (x-\frac {1}{2}\right )}+\frac {75447\,x^2}{32}+\frac {18027\,x^3}{16}+\frac {2997\,x^4}{8}+\frac {243\,x^5}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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