Optimal. Leaf size=41 \[ \frac {3773}{32 (1-2 x)}+\frac {3177 x}{16}+\frac {243 x^2}{4}+\frac {45 x^3}{4}+\frac {3283}{16} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 41, 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 {45 x^3}{4}+\frac {243 x^2}{4}+\frac {3177 x}{16}+\frac {3773}{32 (1-2 x)}+\frac {3283}{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)^3 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac {3177}{16}+\frac {243 x}{2}+\frac {135 x^2}{4}+\frac {3773}{16 (-1+2 x)^2}+\frac {3283}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {3773}{32 (1-2 x)}+\frac {3177 x}{16}+\frac {243 x^2}{4}+\frac {45 x^3}{4}+\frac {3283}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 41, normalized size = 1.00 \begin {gather*} \frac {-65-13770 x+10764 x^2+3528 x^3+720 x^4+6566 (-1+2 x) \log (1-2 x)}{-32+64 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 32, normalized size = 0.78
method | result | size |
risch | \(\frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}-\frac {3773}{64 \left (-\frac {1}{2}+x \right )}+\frac {3283 \ln \left (-1+2 x \right )}{16}\) | \(30\) |
default | \(\frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}-\frac {3773}{32 \left (-1+2 x \right )}+\frac {3283 \ln \left (-1+2 x \right )}{16}\) | \(32\) |
norman | \(\frac {-\frac {3475}{8} x +\frac {2691}{8} x^{2}+\frac {441}{4} x^{3}+\frac {45}{2} x^{4}}{-1+2 x}+\frac {3283 \ln \left (-1+2 x \right )}{16}\) | \(37\) |
meijerg | \(\frac {98 x}{1-2 x}+\frac {3283 \ln \left (1-2 x \right )}{16}+\frac {57 x \left (-6 x +6\right )}{2 \left (1-2 x \right )}+\frac {351 x \left (-8 x^{2}-12 x +12\right )}{32 \left (1-2 x \right )}+\frac {9 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{16 \left (1-2 x \right )}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 31, normalized size = 0.76 \begin {gather*} \frac {45}{4} \, x^{3} + \frac {243}{4} \, x^{2} + \frac {3177}{16} \, x - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} + \frac {3283}{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 = 1.01, size = 42, normalized size = 1.02 \begin {gather*} \frac {720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 6354 \, x - 3773}{32 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 34, normalized size = 0.83 \begin {gather*} \frac {45 x^{3}}{4} + \frac {243 x^{2}}{4} + \frac {3177 x}{16} + \frac {3283 \log {\left (2 x - 1 \right )}}{16} - \frac {3773}{64 x - 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.98, size = 57, normalized size = 1.39 \begin {gather*} \frac {9}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {69}{2 \, x - 1} + \frac {476}{{\left (2 \, x - 1\right )}^{2}} + 5\right )} - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} - \frac {3283}{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 = 29, normalized size = 0.71 \begin {gather*} \frac {3177\,x}{16}+\frac {3283\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {3773}{64\,\left (x-\frac {1}{2}\right )}+\frac {243\,x^2}{4}+\frac {45\,x^3}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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