Optimal. Leaf size=37 \[ -\frac {27 x}{50}-\frac {1}{1375 (5 x+3)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (5 x+3)}{15125} \]
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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} \[ -\frac {27 x}{50}-\frac {1}{1375 (5 x+3)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (5 x+3)}{15125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {27}{50}-\frac {343}{242 (-1+2 x)}+\frac {1}{275 (3+5 x)^2}+\frac {101}{3025 (3+5 x)}\right ) \, dx\\ &=-\frac {27 x}{50}-\frac {1}{1375 (3+5 x)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (3+5 x)}{15125}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 37, normalized size = 1.00 \[ \frac {16335 (1-2 x)-\frac {44}{5 x+3}-42875 \log (1-2 x)+404 \log (10 x+6)}{60500} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 45, normalized size = 1.22 \[ -\frac {163350 \, x^{2} - 404 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 42875 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 98010 \, x + 44}{60500 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 47, normalized size = 1.27 \[ -\frac {27}{50} \, x - \frac {1}{1375 \, {\left (5 \, x + 3\right )}} + \frac {351}{500} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {343}{484} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) - \frac {81}{250} \]
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 \[ -\frac {27 x}{50}-\frac {343 \ln \left (2 x -1\right )}{484}+\frac {101 \ln \left (5 x +3\right )}{15125}-\frac {1}{1375 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 29, normalized size = 0.78 \[ -\frac {27}{50} \, x - \frac {1}{1375 \, {\left (5 \, x + 3\right )}} + \frac {101}{15125} \, \log \left (5 \, x + 3\right ) - \frac {343}{484} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 25, normalized size = 0.68 \[ \frac {101\,\ln \left (x+\frac {3}{5}\right )}{15125}-\frac {343\,\ln \left (x-\frac {1}{2}\right )}{484}-\frac {27\,x}{50}-\frac {1}{6875\,\left (x+\frac {3}{5}\right )} \]
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 \[ - \frac {27 x}{50} - \frac {343 \log {\left (x - \frac {1}{2} \right )}}{484} + \frac {101 \log {\left (x + \frac {3}{5} \right )}}{15125} - \frac {1}{6875 x + 4125} \]
Verification of antiderivative is not currently implemented for this CAS.
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