Optimal. Leaf size=43 \[ \frac {1}{378 (2+3 x)^2}-\frac {103}{1323 (2+3 x)}-\frac {1331}{686} \log (1-2 x)-\frac {3469 \log (2+3 x)}{9261} \]
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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 {103}{1323 (3 x+2)}+\frac {1}{378 (3 x+2)^2}-\frac {1331}{686} \log (1-2 x)-\frac {3469 \log (3 x+2)}{9261} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^3} \, dx &=\int \left (-\frac {1331}{343 (-1+2 x)}-\frac {1}{63 (2+3 x)^3}+\frac {103}{441 (2+3 x)^2}-\frac {3469}{3087 (2+3 x)}\right ) \, dx\\ &=\frac {1}{378 (2+3 x)^2}-\frac {103}{1323 (2+3 x)}-\frac {1331}{686} \log (1-2 x)-\frac {3469 \log (2+3 x)}{9261}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {-\frac {21 (135+206 x)}{(2+3 x)^2}-35937 \log (1-2 x)-6938 \log (4+6 x)}{18522} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {-\frac {103 x}{441}-\frac {15}{98}}{\left (2+3 x \right )^{2}}-\frac {1331 \ln \left (-1+2 x \right )}{686}-\frac {3469 \ln \left (2+3 x \right )}{9261}\) | \(32\) |
norman | \(\frac {\frac {199}{882} x +\frac {135}{392} x^{2}}{\left (2+3 x \right )^{2}}-\frac {1331 \ln \left (-1+2 x \right )}{686}-\frac {3469 \ln \left (2+3 x \right )}{9261}\) | \(35\) |
default | \(-\frac {1331 \ln \left (-1+2 x \right )}{686}+\frac {1}{378 \left (2+3 x \right )^{2}}-\frac {103}{1323 \left (2+3 x \right )}-\frac {3469 \ln \left (2+3 x \right )}{9261}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 36, normalized size = 0.84 \begin {gather*} -\frac {206 \, x + 135}{882 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {3469}{9261} \, \log \left (3 \, x + 2\right ) - \frac {1331}{686} \, \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 = 0.45, size = 55, normalized size = 1.28 \begin {gather*} -\frac {6938 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 35937 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 4326 \, x + 2835}{18522 \, {\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 = 0.09, size = 36, normalized size = 0.84 \begin {gather*} - \frac {206 x + 135}{7938 x^{2} + 10584 x + 3528} - \frac {1331 \log {\left (x - \frac {1}{2} \right )}}{686} - \frac {3469 \log {\left (x + \frac {2}{3} \right )}}{9261} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.43, size = 33, normalized size = 0.77 \begin {gather*} -\frac {206 \, x + 135}{882 \, {\left (3 \, x + 2\right )}^{2}} - \frac {3469}{9261} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1331}{686} \, \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 = 1.13, size = 30, normalized size = 0.70 \begin {gather*} -\frac {1331\,\ln \left (x-\frac {1}{2}\right )}{686}-\frac {3469\,\ln \left (x+\frac {2}{3}\right )}{9261}-\frac {\frac {103\,x}{3969}+\frac {5}{294}}{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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