Optimal. Leaf size=26 \[ \frac {4 x}{15}-\frac {49}{9} \log (2+3 x)+\frac {121}{25} \log (3+5 x) \]
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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 {4 x}{15}-\frac {49}{9} \log (3 x+2)+\frac {121}{25} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 84
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac {4}{15}-\frac {49}{3 (2+3 x)}+\frac {121}{5 (3+5 x)}\right ) \, dx\\ &=\frac {4 x}{15}-\frac {49}{9} \log (2+3 x)+\frac {121}{25} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.04 \begin {gather*} \frac {1}{225} (40+60 x-1225 \log (2+3 x)+1089 \log (-3 (3+5 x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 21, normalized size = 0.81
method | result | size |
default | \(\frac {4 x}{15}-\frac {49 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{25}\) | \(21\) |
norman | \(\frac {4 x}{15}-\frac {49 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{25}\) | \(21\) |
risch | \(\frac {4 x}{15}-\frac {49 \ln \left (2+3 x \right )}{9}+\frac {121 \ln \left (3+5 x \right )}{25}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 20, normalized size = 0.77 \begin {gather*} \frac {4}{15} \, x + \frac {121}{25} \, \log \left (5 \, x + 3\right ) - \frac {49}{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 = 0.43, size = 20, normalized size = 0.77 \begin {gather*} \frac {4}{15} \, x + \frac {121}{25} \, \log \left (5 \, x + 3\right ) - \frac {49}{9} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 24, normalized size = 0.92 \begin {gather*} \frac {4 x}{15} + \frac {121 \log {\left (x + \frac {3}{5} \right )}}{25} - \frac {49 \log {\left (x + \frac {2}{3} \right )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 22, normalized size = 0.85 \begin {gather*} \frac {4}{15} \, x + \frac {121}{25} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {49}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 16, normalized size = 0.62 \begin {gather*} \frac {4\,x}{15}-\frac {49\,\ln \left (x+\frac {2}{3}\right )}{9}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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