Optimal. Leaf size=21 \[ -\frac {7}{3} \log (2+3 x)+\frac {11}{5} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {11}{5} \log (5 x+3)-\frac {7}{3} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x) (3+5 x)} \, dx &=\int \left (-\frac {7}{2+3 x}+\frac {11}{3+5 x}\right ) \, dx\\ &=-\frac {7}{3} \log (2+3 x)+\frac {11}{5} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} -\frac {7}{3} \log (2+3 x)+\frac {11}{5} \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 18, normalized size = 0.86
method | result | size |
default | \(-\frac {7 \ln \left (2+3 x \right )}{3}+\frac {11 \ln \left (3+5 x \right )}{5}\) | \(18\) |
norman | \(-\frac {7 \ln \left (2+3 x \right )}{3}+\frac {11 \ln \left (3+5 x \right )}{5}\) | \(18\) |
risch | \(-\frac {7 \ln \left (2+3 x \right )}{3}+\frac {11 \ln \left (3+5 x \right )}{5}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 0.81 \begin {gather*} \frac {11}{5} \, \log \left (5 \, x + 3\right ) - \frac {7}{3} \, \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 = 0.88, size = 17, normalized size = 0.81 \begin {gather*} \frac {11}{5} \, \log \left (5 \, x + 3\right ) - \frac {7}{3} \, \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 = 19, normalized size = 0.90 \begin {gather*} \frac {11 \log {\left (x + \frac {3}{5} \right )}}{5} - \frac {7 \log {\left (x + \frac {2}{3} \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.62, size = 19, normalized size = 0.90 \begin {gather*} \frac {11}{5} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {7}{3} \, \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 = 0.06, size = 13, normalized size = 0.62 \begin {gather*} \frac {11\,\ln \left (x+\frac {3}{5}\right )}{5}-\frac {7\,\ln \left (x+\frac {2}{3}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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