Optimal. Leaf size=32 \[ \frac {49}{9 (2+3 x)}-\frac {217}{9} \log (2+3 x)+\frac {121}{5} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 32, 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 {49}{9 (3 x+2)}-\frac {217}{9} \log (3 x+2)+\frac {121}{5} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac {49}{3 (2+3 x)^2}-\frac {217}{3 (2+3 x)}+\frac {121}{3+5 x}\right ) \, dx\\ &=\frac {49}{9 (2+3 x)}-\frac {217}{9} \log (2+3 x)+\frac {121}{5} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 32, normalized size = 1.00 \begin {gather*} \frac {49}{18+27 x}-\frac {217}{9} \log (5 (2+3 x))+\frac {121}{5} \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 27, normalized size = 0.84
method | result | size |
risch | \(\frac {49}{27 \left (\frac {2}{3}+x \right )}-\frac {217 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{5}\) | \(25\) |
default | \(\frac {49}{9 \left (2+3 x \right )}-\frac {217 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{5}\) | \(27\) |
norman | \(-\frac {49 x}{6 \left (2+3 x \right )}-\frac {217 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{5}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 26, normalized size = 0.81 \begin {gather*} \frac {49}{9 \, {\left (3 \, x + 2\right )}} + \frac {121}{5} \, \log \left (5 \, x + 3\right ) - \frac {217}{9} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 37, normalized size = 1.16 \begin {gather*} \frac {1089 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1085 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 245}{45 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 26, normalized size = 0.81 \begin {gather*} \frac {121 \log {\left (x + \frac {3}{5} \right )}}{5} - \frac {217 \log {\left (x + \frac {2}{3} \right )}}{9} + \frac {49}{27 x + 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.21, size = 43, normalized size = 1.34 \begin {gather*} \frac {49}{9 \, {\left (3 \, x + 2\right )}} - \frac {4}{45} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {121}{5} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 22, normalized size = 0.69 \begin {gather*} \frac {121\,\ln \left (x+\frac {3}{5}\right )}{5}-\frac {217\,\ln \left (x+\frac {2}{3}\right )}{9}+\frac {49}{27\,\left (x+\frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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