Optimal. Leaf size=43 \[ \frac {343}{484 (1-2 x)}-\frac {1}{3025 (3+5 x)}+\frac {1421 \log (1-2 x)}{5324}+\frac {103 \log (3+5 x)}{33275} \]
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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 {343}{484 (1-2 x)}-\frac {1}{3025 (5 x+3)}+\frac {1421 \log (1-2 x)}{5324}+\frac {103 \log (5 x+3)}{33275} \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)^2} \, dx &=\int \left (\frac {343}{242 (-1+2 x)^2}+\frac {1421}{2662 (-1+2 x)}+\frac {1}{605 (3+5 x)^2}+\frac {103}{6655 (3+5 x)}\right ) \, dx\\ &=\frac {343}{484 (1-2 x)}-\frac {1}{3025 (3+5 x)}+\frac {1421 \log (1-2 x)}{5324}+\frac {103 \log (3+5 x)}{33275}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 40, normalized size = 0.93 \begin {gather*} \frac {-\frac {11 (25721+42883 x)}{-3+x+10 x^2}+35525 \log (3-6 x)+412 \log (-3 (3+5 x))}{133100} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
default | \(-\frac {343}{484 \left (-1+2 x \right )}+\frac {1421 \ln \left (-1+2 x \right )}{5324}-\frac {1}{3025 \left (3+5 x \right )}+\frac {103 \ln \left (3+5 x \right )}{33275}\) | \(36\) |
risch | \(\frac {-\frac {42883 x}{12100}-\frac {25721}{12100}}{\left (3+5 x \right ) \left (-1+2 x \right )}+\frac {1421 \ln \left (-1+2 x \right )}{5324}+\frac {103 \ln \left (3+5 x \right )}{33275}\) | \(39\) |
norman | \(\frac {\frac {42883 x^{2}}{1210}-\frac {15437}{1210}}{\left (3+5 x \right ) \left (-1+2 x \right )}+\frac {1421 \ln \left (-1+2 x \right )}{5324}+\frac {103 \ln \left (3+5 x \right )}{33275}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 34, normalized size = 0.79 \begin {gather*} -\frac {42883 \, x + 25721}{12100 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {103}{33275} \, \log \left (5 \, x + 3\right ) + \frac {1421}{5324} \, \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 = 0.40, size = 49, normalized size = 1.14 \begin {gather*} \frac {412 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 35525 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 471713 \, x - 282931}{133100 \, {\left (10 \, x^{2} + x - 3\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 {- 42883 x - 25721}{121000 x^{2} + 12100 x - 36300} + \frac {1421 \log {\left (x - \frac {1}{2} \right )}}{5324} + \frac {103 \log {\left (x + \frac {3}{5} \right )}}{33275} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.63, size = 58, normalized size = 1.35 \begin {gather*} -\frac {1}{3025 \, {\left (5 \, x + 3\right )}} + \frac {1715}{2662 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {27}{100} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {1421}{5324} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.14, size = 30, normalized size = 0.70 \begin {gather*} \frac {1421\,\ln \left (x-\frac {1}{2}\right )}{5324}+\frac {103\,\ln \left (x+\frac {3}{5}\right )}{33275}-\frac {\frac {42883\,x}{121000}+\frac {25721}{121000}}{x^2+\frac {x}{10}-\frac {3}{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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