Optimal. Leaf size=37 \[ -\frac {8 x}{45}+\frac {343}{27 (3 x+2)}-\frac {1421}{27} \log (3 x+2)+\frac {1331}{25} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 37, 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 = {88} \[ -\frac {8 x}{45}+\frac {343}{27 (3 x+2)}-\frac {1421}{27} \log (3 x+2)+\frac {1331}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac {8}{45}-\frac {343}{9 (2+3 x)^2}-\frac {1421}{9 (2+3 x)}+\frac {1331}{5 (3+5 x)}\right ) \, dx\\ &=-\frac {8 x}{45}+\frac {343}{27 (2+3 x)}-\frac {1421}{27} \log (2+3 x)+\frac {1331}{25} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 36, normalized size = 0.97 \[ \frac {1}{675} \left (-120 x+\frac {8575}{3 x+2}-35525 \log (5 (3 x+2))+35937 \log (5 x+3)-72\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 45, normalized size = 1.22 \[ -\frac {360 \, x^{2} - 35937 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) + 35525 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 240 \, x - 8575}{675 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 47, normalized size = 1.27 \[ -\frac {8}{45} \, x + \frac {343}{27 \, {\left (3 \, x + 2\right )}} - \frac {412}{675} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {1331}{25} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {16}{135} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 30, normalized size = 0.81 \[ -\frac {8 x}{45}-\frac {1421 \ln \left (3 x +2\right )}{27}+\frac {1331 \ln \left (5 x +3\right )}{25}+\frac {343}{27 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 29, normalized size = 0.78 \[ -\frac {8}{45} \, x + \frac {343}{27 \, {\left (3 \, x + 2\right )}} + \frac {1331}{25} \, \log \left (5 \, x + 3\right ) - \frac {1421}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 25, normalized size = 0.68 \[ \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{25}-\frac {1421\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {8\,x}{45}+\frac {343}{81\,\left (x+\frac {2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 31, normalized size = 0.84 \[ - \frac {8 x}{45} + \frac {1331 \log {\left (x + \frac {3}{5} \right )}}{25} - \frac {1421 \log {\left (x + \frac {2}{3} \right )}}{27} + \frac {343}{81 x + 54} \]
Verification of antiderivative is not currently implemented for this CAS.
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