Optimal. Leaf size=43 \[ -\frac {1}{126 (2+3 x)^2}+\frac {68}{441 (2+3 x)}-\frac {121}{343} \log (1-2 x)+\frac {121}{343} \log (2+3 x) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {68}{441 (3 x+2)}-\frac {1}{126 (3 x+2)^2}-\frac {121}{343} \log (1-2 x)+\frac {121}{343} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x) (2+3 x)^3} \, dx &=\int \left (-\frac {242}{343 (-1+2 x)}+\frac {1}{21 (2+3 x)^3}-\frac {68}{147 (2+3 x)^2}+\frac {363}{343 (2+3 x)}\right ) \, dx\\ &=-\frac {1}{126 (2+3 x)^2}+\frac {68}{441 (2+3 x)}-\frac {121}{343} \log (1-2 x)+\frac {121}{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 (265+408 x)}{(2+3 x)^2}-2178 \log (1-2 x)+2178 \log (4+6 x)}{6174} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {68 x}{147}+\frac {265}{882}}{\left (2+3 x \right )^{2}}-\frac {121 \ln \left (-1+2 x \right )}{343}+\frac {121 \ln \left (2+3 x \right )}{343}\) | \(32\) |
norman | \(\frac {-\frac {265}{392} x^{2}-\frac {43}{98} x}{\left (2+3 x \right )^{2}}-\frac {121 \ln \left (-1+2 x \right )}{343}+\frac {121 \ln \left (2+3 x \right )}{343}\) | \(35\) |
default | \(-\frac {121 \ln \left (-1+2 x \right )}{343}-\frac {1}{126 \left (2+3 x \right )^{2}}+\frac {68}{441 \left (2+3 x \right )}+\frac {121 \ln \left (2+3 x \right )}{343}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 36, normalized size = 0.84 \begin {gather*} \frac {408 \, x + 265}{882 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {121}{343} \, \log \left (3 \, x + 2\right ) - \frac {121}{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 = 0.39, size = 55, normalized size = 1.28 \begin {gather*} \frac {2178 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 2178 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 2856 \, x + 1855}{6174 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 36, normalized size = 0.84 \begin {gather*} - \frac {- 408 x - 265}{7938 x^{2} + 10584 x + 3528} - \frac {121 \log {\left (x - \frac {1}{2} \right )}}{343} + \frac {121 \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 = 0.61, size = 33, normalized size = 0.77 \begin {gather*} \frac {408 \, x + 265}{882 \, {\left (3 \, x + 2\right )}^{2}} + \frac {121}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {121}{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 {242\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{343}+\frac {\frac {68\,x}{1323}+\frac {265}{7938}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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