Optimal. Leaf size=37 \[ \frac {343}{88 (1-2 x)}+\frac {27 x}{20}+\frac {392}{121} \log (1-2 x)+\frac {\log (3+5 x)}{3025} \]
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Rubi [A]
time = 0.01, 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 = {90}
\begin {gather*} \frac {27 x}{20}+\frac {343}{88 (1-2 x)}+\frac {392}{121} \log (1-2 x)+\frac {\log (5 x+3)}{3025} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {27}{20}+\frac {343}{44 (-1+2 x)^2}+\frac {784}{121 (-1+2 x)}+\frac {1}{605 (3+5 x)}\right ) \, dx\\ &=\frac {343}{88 (1-2 x)}+\frac {27 x}{20}+\frac {392}{121} \log (1-2 x)+\frac {\log (3+5 x)}{3025}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 37, normalized size = 1.00 \begin {gather*} \frac {\frac {94325}{1-2 x}+6534 (3+5 x)+78400 \log (5-10 x)+8 \log (3+5 x)}{24200} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 30, normalized size = 0.81
method | result | size |
risch | \(\frac {27 x}{20}-\frac {343}{176 \left (-\frac {1}{2}+x \right )}+\frac {392 \ln \left (-1+2 x \right )}{121}+\frac {\ln \left (3+5 x \right )}{3025}\) | \(28\) |
default | \(\frac {27 x}{20}-\frac {343}{88 \left (-1+2 x \right )}+\frac {392 \ln \left (-1+2 x \right )}{121}+\frac {\ln \left (3+5 x \right )}{3025}\) | \(30\) |
norman | \(\frac {-\frac {503}{55} x +\frac {27}{10} x^{2}}{-1+2 x}+\frac {392 \ln \left (-1+2 x \right )}{121}+\frac {\ln \left (3+5 x \right )}{3025}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 29, normalized size = 0.78 \begin {gather*} \frac {27}{20} \, x - \frac {343}{88 \, {\left (2 \, x - 1\right )}} + \frac {1}{3025} \, \log \left (5 \, x + 3\right ) + \frac {392}{121} \, \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 = 45, normalized size = 1.22 \begin {gather*} \frac {65340 \, x^{2} + 8 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 78400 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 32670 \, x - 94325}{24200 \, {\left (2 \, 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 = 29, normalized size = 0.78 \begin {gather*} \frac {27 x}{20} + \frac {392 \log {\left (x - \frac {1}{2} \right )}}{121} + \frac {\log {\left (x + \frac {3}{5} \right )}}{3025} - \frac {343}{176 x - 88} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 47, normalized size = 1.27 \begin {gather*} \frac {27}{20} \, x - \frac {343}{88 \, {\left (2 \, x - 1\right )}} - \frac {81}{25} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{3025} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) - \frac {27}{40} \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 = 0.68 \begin {gather*} \frac {27\,x}{20}+\frac {392\,\ln \left (x-\frac {1}{2}\right )}{121}+\frac {\ln \left (x+\frac {3}{5}\right )}{3025}-\frac {343}{176\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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