Optimal. Leaf size=37 \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]
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Rubi [A] time = 0.015847, antiderivative size = 37, 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} \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{7}{(2+3 x)^3}-\frac{33}{(2+3 x)^2}-\frac{165}{2+3 x}+\frac{275}{3+5 x}\right ) \, dx\\ &=\frac{7}{6 (2+3 x)^2}+\frac{11}{2+3 x}-55 \log (2+3 x)+55 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0200619, size = 35, normalized size = 0.95 \[ \frac{198 x+139}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 36, normalized size = 1. \begin{align*}{\frac{7}{6\, \left ( 2+3\,x \right ) ^{2}}}+11\, \left ( 2+3\,x \right ) ^{-1}-55\,\ln \left ( 2+3\,x \right ) +55\,\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 = 1.15115, size = 49, normalized size = 1.32 \begin{align*} \frac{198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + 55 \, \log \left (5 \, x + 3\right ) - 55 \, \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 = 1.69812, size = 154, normalized size = 4.16 \begin{align*} \frac{330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127344, size = 31, normalized size = 0.84 \begin{align*} \frac{198 x + 139}{54 x^{2} + 72 x + 24} + 55 \log{\left (x + \frac{3}{5} \right )} - 55 \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 = 2.43496, size = 45, normalized size = 1.22 \begin{align*} \frac{198 \, x + 139}{6 \,{\left (3 \, x + 2\right )}^{2}} + 55 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 55 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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