Optimal. Leaf size=27 \[ \frac {77}{8 (1-2 x)}+\frac {15 x}{4}+\frac {17}{2} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78}
\begin {gather*} \frac {15 x}{4}+\frac {77}{8 (1-2 x)}+\frac {17}{2} \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+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac {15}{4}+\frac {77}{4 (-1+2 x)^2}+\frac {17}{-1+2 x}\right ) \, dx\\ &=\frac {77}{8 (1-2 x)}+\frac {15 x}{4}+\frac {17}{2} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 26, normalized size = 0.96 \begin {gather*} \frac {1}{8} \left (-15+\frac {77}{1-2 x}+30 x+68 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 22, normalized size = 0.81
method | result | size |
risch | \(\frac {15 x}{4}-\frac {77}{16 \left (-\frac {1}{2}+x \right )}+\frac {17 \ln \left (-1+2 x \right )}{2}\) | \(20\) |
default | \(\frac {15 x}{4}-\frac {77}{8 \left (-1+2 x \right )}+\frac {17 \ln \left (-1+2 x \right )}{2}\) | \(22\) |
norman | \(\frac {-23 x +\frac {15}{2} x^{2}}{-1+2 x}+\frac {17 \ln \left (-1+2 x \right )}{2}\) | \(27\) |
meijerg | \(\frac {31 x}{2 \left (1-2 x \right )}+\frac {17 \ln \left (1-2 x \right )}{2}+\frac {5 x \left (-6 x +6\right )}{4 \left (1-2 x \right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 21, normalized size = 0.78 \begin {gather*} \frac {15}{4} \, x - \frac {77}{8 \, {\left (2 \, x - 1\right )}} + \frac {17}{2} \, \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 = 1.36, size = 32, normalized size = 1.19 \begin {gather*} \frac {60 \, x^{2} + 68 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 30 \, x - 77}{8 \, {\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 = 20, normalized size = 0.74 \begin {gather*} \frac {15 x}{4} + \frac {17 \log {\left (2 x - 1 \right )}}{2} - \frac {77}{16 x - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.09, size = 32, normalized size = 1.19 \begin {gather*} \frac {15}{4} \, x - \frac {77}{8 \, {\left (2 \, x - 1\right )}} - \frac {17}{2} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) - \frac {15}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 19, normalized size = 0.70 \begin {gather*} \frac {15\,x}{4}+\frac {17\,\ln \left (x-\frac {1}{2}\right )}{2}-\frac {77}{16\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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