Optimal. Leaf size=33 \[ \frac {121}{16 (1-2 x)^2}-\frac {55}{4 (1-2 x)}-\frac {25}{8} \log (1-2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 33, 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 {55}{4 (1-2 x)}+\frac {121}{16 (1-2 x)^2}-\frac {25}{8} \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)^3} \, dx &=\int \left (-\frac {121}{4 (-1+2 x)^3}-\frac {55}{2 (-1+2 x)^2}-\frac {25}{4 (-1+2 x)}\right ) \, dx\\ &=\frac {121}{16 (1-2 x)^2}-\frac {55}{4 (1-2 x)}-\frac {25}{8} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 33, normalized size = 1.00 \begin {gather*} \frac {121}{16 (1-2 x)^2}-\frac {55}{4 (1-2 x)}-\frac {25}{8} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 28, normalized size = 0.85
method | result | size |
risch | \(\frac {\frac {55 x}{2}-\frac {99}{16}}{\left (-1+2 x \right )^{2}}-\frac {25 \ln \left (-1+2 x \right )}{8}\) | \(24\) |
norman | \(\frac {\frac {11}{4} x +\frac {99}{4} x^{2}}{\left (-1+2 x \right )^{2}}-\frac {25 \ln \left (-1+2 x \right )}{8}\) | \(27\) |
default | \(\frac {55}{4 \left (-1+2 x \right )}+\frac {121}{16 \left (-1+2 x \right )^{2}}-\frac {25 \ln \left (-1+2 x \right )}{8}\) | \(28\) |
meijerg | \(\frac {9 x \left (2-2 x \right )}{2 \left (1-2 x \right )^{2}}+\frac {15 x^{2}}{\left (1-2 x \right )^{2}}-\frac {25 x \left (-18 x +6\right )}{24 \left (1-2 x \right )^{2}}-\frac {25 \ln \left (1-2 x \right )}{8}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 28, normalized size = 0.85 \begin {gather*} \frac {11 \, {\left (40 \, x - 9\right )}}{16 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {25}{8} \, \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 = 0.39, size = 37, normalized size = 1.12 \begin {gather*} -\frac {50 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 440 \, x + 99}{16 \, {\left (4 \, x^{2} - 4 \, 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 = 26, normalized size = 0.79 \begin {gather*} - \frac {99 - 440 x}{64 x^{2} - 64 x + 16} - \frac {25 \log {\left (2 x - 1 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 24, normalized size = 0.73 \begin {gather*} \frac {11 \, {\left (40 \, x - 9\right )}}{16 \, {\left (2 \, x - 1\right )}^{2}} - \frac {25}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 23, normalized size = 0.70 \begin {gather*} \frac {\frac {55\,x}{8}-\frac {99}{64}}{x^2-x+\frac {1}{4}}-\frac {25\,\ln \left (x-\frac {1}{2}\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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