Optimal. Leaf size=70 \[ \frac{1375}{3 x+2}+\frac{275}{2 (3 x+2)^2}+\frac{55}{3 (3 x+2)^3}+\frac{11}{4 (3 x+2)^4}+\frac{7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3) \]
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Rubi [A] time = 0.025152, antiderivative size = 70, 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} \[ \frac{1375}{3 x+2}+\frac{275}{2 (3 x+2)^2}+\frac{55}{3 (3 x+2)^3}+\frac{11}{4 (3 x+2)^4}+\frac{7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^6 (3+5 x)} \, dx &=\int \left (-\frac{7}{(2+3 x)^6}-\frac{33}{(2+3 x)^5}-\frac{165}{(2+3 x)^4}-\frac{825}{(2+3 x)^3}-\frac{4125}{(2+3 x)^2}-\frac{20625}{2+3 x}+\frac{34375}{3+5 x}\right ) \, dx\\ &=\frac{7}{15 (2+3 x)^5}+\frac{11}{4 (2+3 x)^4}+\frac{55}{3 (2+3 x)^3}+\frac{275}{2 (2+3 x)^2}+\frac{1375}{2+3 x}-6875 \log (2+3 x)+6875 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0304622, size = 50, normalized size = 0.71 \[ \frac{2227500 x^4+6014250 x^3+6091800 x^2+2743565 x+463586}{20 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 63, normalized size = 0.9 \begin{align*}{\frac{7}{15\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{11}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{55}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{275}{2\, \left ( 2+3\,x \right ) ^{2}}}+1375\, \left ( 2+3\,x \right ) ^{-1}-6875\,\ln \left ( 2+3\,x \right ) +6875\,\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 = 2.31021, size = 89, normalized size = 1.27 \begin{align*} \frac{2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 6875 \, \log \left (5 \, x + 3\right ) - 6875 \, \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 = 1.69312, size = 371, normalized size = 5.3 \begin{align*} \frac{2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 137500 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 137500 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 2743565 \, x + 463586}{20 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.172333, size = 61, normalized size = 0.87 \begin{align*} \frac{2227500 x^{4} + 6014250 x^{3} + 6091800 x^{2} + 2743565 x + 463586}{4860 x^{5} + 16200 x^{4} + 21600 x^{3} + 14400 x^{2} + 4800 x + 640} + 6875 \log{\left (x + \frac{3}{5} \right )} - 6875 \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 = 2.47694, size = 65, normalized size = 0.93 \begin{align*} \frac{2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \,{\left (3 \, x + 2\right )}^{5}} + 6875 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6875 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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