Optimal. Leaf size=43 \[ \frac {11}{28 (1-2 x)^2}-\frac {1}{49 (1-2 x)}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 {1}{49 (1-2 x)}+\frac {11}{28 (1-2 x)^2}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac {11}{7 (-1+2 x)^3}-\frac {2}{49 (-1+2 x)^2}+\frac {6}{343 (-1+2 x)}-\frac {9}{343 (2+3 x)}\right ) \, dx\\ &=\frac {11}{28 (1-2 x)^2}-\frac {1}{49 (1-2 x)}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {\frac {7 (73+8 x)}{(1-2 x)^2}+12 \log (1-2 x)-12 \log (4+6 x)}{1372} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {2 x}{49}+\frac {73}{196}}{\left (-1+2 x \right )^{2}}+\frac {3 \ln \left (-1+2 x \right )}{343}-\frac {3 \ln \left (2+3 x \right )}{343}\) | \(32\) |
norman | \(\frac {\frac {75}{49} x -\frac {73}{49} x^{2}}{\left (-1+2 x \right )^{2}}+\frac {3 \ln \left (-1+2 x \right )}{343}-\frac {3 \ln \left (2+3 x \right )}{343}\) | \(35\) |
default | \(\frac {11}{28 \left (-1+2 x \right )^{2}}+\frac {1}{-49+98 x}+\frac {3 \ln \left (-1+2 x \right )}{343}-\frac {3 \ln \left (2+3 x \right )}{343}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 36, normalized size = 0.84 \begin {gather*} \frac {8 \, x + 73}{196 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {3}{343} \, \log \left (3 \, x + 2\right ) + \frac {3}{343} \, \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 = 0.42, size = 55, normalized size = 1.28 \begin {gather*} -\frac {12 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 12 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 56 \, x - 511}{1372 \, {\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 = 0.05, size = 36, normalized size = 0.84 \begin {gather*} - \frac {- 8 x - 73}{784 x^{2} - 784 x + 196} + \frac {3 \log {\left (x - \frac {1}{2} \right )}}{343} - \frac {3 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.80, size = 33, normalized size = 0.77 \begin {gather*} \frac {8 \, x + 73}{196 \, {\left (2 \, x - 1\right )}^{2}} - \frac {3}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {3}{343} \, \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 = 0.04, size = 25, normalized size = 0.58 \begin {gather*} \frac {\frac {x}{98}+\frac {73}{784}}{x^2-x+\frac {1}{4}}-\frac {6\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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