Optimal. Leaf size=48 \[ \frac{55}{3 x+2}+\frac{11}{2 (3 x+2)^2}+\frac{7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3) \]
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Rubi [A] time = 0.0191768, antiderivative size = 48, 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} \[ \frac{55}{3 x+2}+\frac{11}{2 (3 x+2)^2}+\frac{7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^4 (3+5 x)} \, dx &=\int \left (-\frac{7}{(2+3 x)^4}-\frac{33}{(2+3 x)^3}-\frac{165}{(2+3 x)^2}-\frac{825}{2+3 x}+\frac{1375}{3+5 x}\right ) \, dx\\ &=\frac{7}{9 (2+3 x)^3}+\frac{11}{2 (2+3 x)^2}+\frac{55}{2+3 x}-275 \log (2+3 x)+275 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0242245, size = 40, normalized size = 0.83 \[ \frac{8910 x^2+12177 x+4172}{18 (3 x+2)^3}-275 \log (3 x+2)+275 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 45, normalized size = 0.9 \begin{align*}{\frac{7}{9\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{11}{2\, \left ( 2+3\,x \right ) ^{2}}}+55\, \left ( 2+3\,x \right ) ^{-1}-275\,\ln \left ( 2+3\,x \right ) +275\,\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 = 1.16814, size = 62, normalized size = 1.29 \begin{align*} \frac{8910 \, x^{2} + 12177 \, x + 4172}{18 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 275 \, \log \left (5 \, x + 3\right ) - 275 \, \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 = 1.71802, size = 217, normalized size = 4.52 \begin{align*} \frac{8910 \, x^{2} + 4950 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 4950 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 12177 \, x + 4172}{18 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.143739, size = 41, normalized size = 0.85 \begin{align*} \frac{8910 x^{2} + 12177 x + 4172}{486 x^{3} + 972 x^{2} + 648 x + 144} + 275 \log{\left (x + \frac{3}{5} \right )} - 275 \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 = 2.25271, size = 51, normalized size = 1.06 \begin{align*} \frac{8910 \, x^{2} + 12177 \, x + 4172}{18 \,{\left (3 \, x + 2\right )}^{3}} + 275 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 275 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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