Optimal. Leaf size=75 \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3) \]
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Rubi [A] time = 0.0382755, antiderivative size = 75, 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} \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^3} \, dx &=\int \left (-\frac{63}{(2+3 x)^5}-\frac{927}{(2+3 x)^4}-\frac{9180}{(2+3 x)^3}-\frac{76050}{(2+3 x)^2}-\frac{568125}{2+3 x}+\frac{6875}{(3+5 x)^3}-\frac{104375}{(3+5 x)^2}+\frac{946875}{3+5 x}\right ) \, dx\\ &=\frac{21}{4 (2+3 x)^4}+\frac{103}{(2+3 x)^3}+\frac{1530}{(2+3 x)^2}+\frac{25350}{2+3 x}-\frac{1375}{2 (3+5 x)^2}+\frac{20875}{3+5 x}-189375 \log (2+3 x)+189375 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0281883, size = 77, normalized size = 1.03 \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 72, normalized size = 1. \begin{align*}{\frac{21}{4\, \left ( 2+3\,x \right ) ^{4}}}+103\, \left ( 2+3\,x \right ) ^{-3}+1530\, \left ( 2+3\,x \right ) ^{-2}+25350\, \left ( 2+3\,x \right ) ^{-1}-{\frac{1375}{2\, \left ( 3+5\,x \right ) ^{2}}}+20875\, \left ( 3+5\,x \right ) ^{-1}-189375\,\ln \left ( 2+3\,x \right ) +189375\,\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 = 1.10176, size = 103, normalized size = 1.37 \begin{align*} \frac{102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 89085434 \, x + 11492725}{4 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 189375 \, \log \left (5 \, x + 3\right ) - 189375 \, \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 = 1.59953, size = 477, normalized size = 6.36 \begin{align*} \frac{102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 757500 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 757500 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 89085434 \, x + 11492725}{4 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.188315, size = 71, normalized size = 0.95 \begin{align*} \frac{102262500 x^{5} + 330648750 x^{4} + 427381500 x^{3} + 276035525 x^{2} + 89085434 x + 11492725}{8100 x^{6} + 31320 x^{5} + 50436 x^{4} + 43296 x^{3} + 20896 x^{2} + 5376 x + 576} + 189375 \log{\left (x + \frac{3}{5} \right )} - 189375 \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 = 2.88769, size = 103, normalized size = 1.37 \begin{align*} \frac{25350}{3 \, x + 2} - \frac{9375 \,{\left (\frac{80}{3 \, x + 2} - 367\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{1530}{{\left (3 \, x + 2\right )}^{2}} + \frac{103}{{\left (3 \, x + 2\right )}^{3}} + \frac{21}{4 \,{\left (3 \, x + 2\right )}^{4}} + 189375 \, \log \left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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