Optimal. Leaf size=28 \[ -\frac {11}{5 (3+5 x)}+7 \log (2+3 x)-7 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 28, 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 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3) \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)^2} \, dx &=\int \left (\frac {21}{2+3 x}+\frac {11}{(3+5 x)^2}-\frac {35}{3+5 x}\right ) \, dx\\ &=-\frac {11}{5 (3+5 x)}+7 \log (2+3 x)-7 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 30, normalized size = 1.07 \begin {gather*} -\frac {11}{5 (3+5 x)}+7 \log (5 (2+3 x))-7 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 27, normalized size = 0.96
method | result | size |
risch | \(-\frac {11}{25 \left (x +\frac {3}{5}\right )}+7 \ln \left (2+3 x \right )-7 \ln \left (3+5 x \right )\) | \(25\) |
default | \(-\frac {11}{5 \left (3+5 x \right )}+7 \ln \left (2+3 x \right )-7 \ln \left (3+5 x \right )\) | \(27\) |
norman | \(\frac {11 x}{3 \left (3+5 x \right )}+7 \ln \left (2+3 x \right )-7 \ln \left (3+5 x \right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 26, normalized size = 0.93 \begin {gather*} -\frac {11}{5 \, {\left (5 \, x + 3\right )}} - 7 \, \log \left (5 \, x + 3\right ) + 7 \, \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 = 1.32, size = 37, normalized size = 1.32 \begin {gather*} -\frac {35 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 35 \, {\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 11}{5 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 22, normalized size = 0.79 \begin {gather*} - 7 \log {\left (x + \frac {3}{5} \right )} + 7 \log {\left (x + \frac {2}{3} \right )} - \frac {11}{25 x + 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.75, size = 25, normalized size = 0.89 \begin {gather*} -\frac {11}{5 \, {\left (5 \, x + 3\right )}} + 7 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 18, normalized size = 0.64 \begin {gather*} 14\,\mathrm {atanh}\left (30\,x+19\right )-\frac {11}{25\,\left (x+\frac {3}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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