Optimal. Leaf size=35 \[ -\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3) \]
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Rubi [A] time = 0.0163061, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac{21}{(2+3 x)^2}+\frac{204}{2+3 x}+\frac{55}{(3+5 x)^2}-\frac{340}{3+5 x}\right ) \, dx\\ &=-\frac{7}{2+3 x}-\frac{11}{3+5 x}+68 \log (2+3 x)-68 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0174377, size = 37, normalized size = 1.06 \[ -\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 36, normalized size = 1. \begin{align*} -7\, \left ( 2+3\,x \right ) ^{-1}-11\, \left ( 3+5\,x \right ) ^{-1}+68\,\ln \left ( 2+3\,x \right ) -68\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06285, size = 49, normalized size = 1.4 \begin{align*} -\frac{68 \, x + 43}{15 \, x^{2} + 19 \, x + 6} - 68 \, \log \left (5 \, x + 3\right ) + 68 \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51341, size = 149, normalized size = 4.26 \begin{align*} -\frac{68 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 68 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 68 \, x + 43}{15 \, x^{2} + 19 \, x + 6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125139, size = 31, normalized size = 0.89 \begin{align*} - \frac{68 x + 43}{15 x^{2} + 19 x + 6} - 68 \log{\left (x + \frac{3}{5} \right )} + 68 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.68657, size = 51, normalized size = 1.46 \begin{align*} -\frac{11}{5 \, x + 3} + \frac{105}{\frac{1}{5 \, x + 3} + 3} + 68 \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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