Optimal. Leaf size=28 \[ \frac {7}{3 (2+3 x)}-11 \log (2+3 x)+11 \log (3+5 x) \]
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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 {7}{3 (3 x+2)}-11 \log (3 x+2)+11 \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)^2 (3+5 x)} \, dx &=\int \left (-\frac {7}{(2+3 x)^2}-\frac {33}{2+3 x}+\frac {55}{3+5 x}\right ) \, dx\\ &=\frac {7}{3 (2+3 x)}-11 \log (2+3 x)+11 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 38, normalized size = 1.36 \begin {gather*} \frac {7-33 (2+3 x) \log (2+3 x)+33 (2+3 x) \log (-3 (3+5 x))}{6+9 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 0.96
method | result | size |
risch | \(\frac {7}{9 \left (\frac {2}{3}+x \right )}-11 \ln \left (2+3 x \right )+11 \ln \left (3+5 x \right )\) | \(25\) |
default | \(\frac {7}{3 \left (2+3 x \right )}-11 \ln \left (2+3 x \right )+11 \ln \left (3+5 x \right )\) | \(27\) |
norman | \(-\frac {7 x}{2 \left (2+3 x \right )}-11 \ln \left (2+3 x \right )+11 \ln \left (3+5 x \right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 26, normalized size = 0.93 \begin {gather*} \frac {7}{3 \, {\left (3 \, x + 2\right )}} + 11 \, \log \left (5 \, x + 3\right ) - 11 \, \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 = 0.99, size = 37, normalized size = 1.32 \begin {gather*} \frac {33 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 33 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 7}{3 \, {\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 = 22, normalized size = 0.79 \begin {gather*} 11 \log {\left (x + \frac {3}{5} \right )} - 11 \log {\left (x + \frac {2}{3} \right )} + \frac {7}{9 x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.98, size = 25, normalized size = 0.89 \begin {gather*} \frac {7}{3 \, {\left (3 \, x + 2\right )}} + 11 \, \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 = 0.04, size = 18, normalized size = 0.64 \begin {gather*} \frac {7}{9\,\left (x+\frac {2}{3}\right )}-22\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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