Optimal. Leaf size=27 \[ \frac {121}{8 (1-2 x)}+\frac {25 x}{4}+\frac {55}{4} \log (1-2 x) \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {25 x}{4}+\frac {121}{8 (1-2 x)}+\frac {55}{4} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {25}{4}+\frac {121}{4 (-1+2 x)^2}+\frac {55}{2 (-1+2 x)}\right ) \, dx\\ &=\frac {121}{8 (1-2 x)}+\frac {25 x}{4}+\frac {55}{4} \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 (-25+\frac {121}{1-2 x}+50 x+110 \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 | \(\frac {25 x}{4}-\frac {121}{16 \left (-\frac {1}{2}+x \right )}+\frac {55 \ln \left (-1+2 x \right )}{4}\) | \(20\) |
default | \(\frac {25 x}{4}-\frac {121}{8 \left (-1+2 x \right )}+\frac {55 \ln \left (-1+2 x \right )}{4}\) | \(22\) |
norman | \(\frac {-\frac {73}{2} x +\frac {25}{2} x^{2}}{-1+2 x}+\frac {55 \ln \left (-1+2 x \right )}{4}\) | \(27\) |
meijerg | \(\frac {24 x}{1-2 x}+\frac {55 \ln \left (1-2 x \right )}{4}+\frac {25 x \left (-6 x +6\right )}{12 \left (1-2 x \right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 21, normalized size = 0.78 \begin {gather*} \frac {25}{4} \, x - \frac {121}{8 \, {\left (2 \, x - 1\right )}} + \frac {55}{4} \, \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 = 0.90, size = 32, normalized size = 1.19 \begin {gather*} \frac {100 \, x^{2} + 110 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 50 \, x - 121}{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 = 0.04, size = 20, normalized size = 0.74 \begin {gather*} \frac {25 x}{4} + \frac {55 \log {\left (2 x - 1 \right )}}{4} - \frac {121}{16 x - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.35, size = 32, normalized size = 1.19 \begin {gather*} \frac {25}{4} \, x - \frac {121}{8 \, {\left (2 \, x - 1\right )}} - \frac {55}{4} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) - \frac {25}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.13, size = 19, normalized size = 0.70 \begin {gather*} \frac {25\,x}{4}+\frac {55\,\ln \left (x-\frac {1}{2}\right )}{4}-\frac {121}{16\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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