Optimal. Leaf size=68 \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (5 x+3) \]
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Rubi [A] time = 0.0308254, antiderivative size = 68, 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} \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (5 x+3) \]
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)^2} \, dx &=\int \left (\frac{21}{(2+3 x)^5}+\frac{204}{(2+3 x)^4}+\frac{1515}{(2+3 x)^3}+\frac{10050}{(2+3 x)^2}+\frac{62625}{2+3 x}+\frac{6875}{(3+5 x)^2}-\frac{104375}{3+5 x}\right ) \, dx\\ &=-\frac{7}{4 (2+3 x)^4}-\frac{68}{3 (2+3 x)^3}-\frac{505}{2 (2+3 x)^2}-\frac{3350}{2+3 x}-\frac{1375}{3+5 x}+20875 \log (2+3 x)-20875 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.024527, size = 70, normalized size = 1.03 \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 63, normalized size = 0.9 \begin{align*} -{\frac{7}{4\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{68}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{505}{2\, \left ( 2+3\,x \right ) ^{2}}}-3350\, \left ( 2+3\,x \right ) ^{-1}-1375\, \left ( 3+5\,x \right ) ^{-1}+20875\,\ln \left ( 2+3\,x \right ) -20875\,\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 = 1.08823, size = 89, normalized size = 1.31 \begin{align*} -\frac{6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 7708553 \, x + 1266855}{12 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 20875 \, \log \left (5 \, x + 3\right ) + 20875 \, \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 = 1.53813, size = 385, normalized size = 5.66 \begin{align*} -\frac{6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 250500 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 250500 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 7708553 \, x + 1266855}{12 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.174281, size = 61, normalized size = 0.9 \begin{align*} - \frac{6763500 x^{4} + 17810550 x^{3} + 17580090 x^{2} + 7708553 x + 1266855}{4860 x^{5} + 15876 x^{4} + 20736 x^{3} + 13536 x^{2} + 4416 x + 576} - 20875 \log{\left (x + \frac{3}{5} \right )} + 20875 \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 = 1.66759, size = 90, normalized size = 1.32 \begin{align*} -\frac{1375}{5 \, x + 3} + \frac{375 \,{\left (\frac{26268}{5 \, x + 3} + \frac{10116}{{\left (5 \, x + 3\right )}^{2}} + \frac{1352}{{\left (5 \, x + 3\right )}^{3}} + 23319\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + 20875 \, \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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