Optimal. Leaf size=26 \[ -\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 26, 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 = {84}
\begin {gather*} -\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 84
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {9}{10}-\frac {49}{22 (-1+2 x)}+\frac {1}{55 (3+5 x)}\right ) \, dx\\ &=-\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 31, normalized size = 1.19 \begin {gather*} -\frac {3}{5}-\frac {9 x}{10}-\frac {49}{44} \log (3-6 x)+\frac {1}{275} \log (-3 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 21, normalized size = 0.81
method | result | size |
default | \(-\frac {9 x}{10}-\frac {49 \ln \left (-1+2 x \right )}{44}+\frac {\ln \left (3+5 x \right )}{275}\) | \(21\) |
norman | \(-\frac {9 x}{10}-\frac {49 \ln \left (-1+2 x \right )}{44}+\frac {\ln \left (3+5 x \right )}{275}\) | \(21\) |
risch | \(-\frac {9 x}{10}-\frac {49 \ln \left (-1+2 x \right )}{44}+\frac {\ln \left (3+5 x \right )}{275}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 20, normalized size = 0.77 \begin {gather*} -\frac {9}{10} \, x + \frac {1}{275} \, \log \left (5 \, x + 3\right ) - \frac {49}{44} \, \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 = 0.89, size = 20, normalized size = 0.77 \begin {gather*} -\frac {9}{10} \, x + \frac {1}{275} \, \log \left (5 \, x + 3\right ) - \frac {49}{44} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 0.85 \begin {gather*} - \frac {9 x}{10} - \frac {49 \log {\left (x - \frac {1}{2} \right )}}{44} + \frac {\log {\left (x + \frac {3}{5} \right )}}{275} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.79, size = 22, normalized size = 0.85 \begin {gather*} -\frac {9}{10} \, x + \frac {1}{275} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {49}{44} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 16, normalized size = 0.62 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{275}-\frac {49\,\ln \left (x-\frac {1}{2}\right )}{44}-\frac {9\,x}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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