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 = 0.03, antiderivative size = 68, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.04, 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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fricas [A] time = 0.48, size = 115, normalized size = 1.69 \[ -\frac {6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 250500 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 250500 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 7708553 \, x + 1266855}{12 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 67, normalized size = 0.99 \[ -\frac {1375}{5 \, x + 3} + \frac {375 \, {\left (\frac {26268}{5 \, x + 3} + \frac {10116}{{\left (5 \, x + 3\right )}^{2}} + \frac {1352}{{\left (5 \, x + 3\right )}^{3}} + 23319\right )}}{4 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{4}} + 20875 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 63, normalized size = 0.93 \[ 20875 \ln \left (3 x +2\right )-20875 \ln \left (5 x +3\right )-\frac {7}{4 \left (3 x +2\right )^{4}}-\frac {68}{3 \left (3 x +2\right )^{3}}-\frac {505}{2 \left (3 x +2\right )^{2}}-\frac {3350}{3 x +2}-\frac {1375}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 66, normalized size = 0.97 \[ -\frac {6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 7708553 \, x + 1266855}{12 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 20875 \, \log \left (5 \, x + 3\right ) + 20875 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 56, normalized size = 0.82 \[ 41750\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {4175\,x^4}{3}+\frac {65965\,x^3}{18}+\frac {586003\,x^2}{162}+\frac {7708553\,x}{4860}+\frac {84457}{324}}{x^5+\frac {49\,x^4}{15}+\frac {64\,x^3}{15}+\frac {376\,x^2}{135}+\frac {368\,x}{405}+\frac {16}{135}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 61, normalized size = 0.90 \[ - \frac {6763500 x^{4} + 17810550 x^{3} + 17580090 x^{2} + 7708553 x + 1266855}{4860 x^{5} + 15876 x^{4} + 20736 x^{3} + 13536 x^{2} + 4416 x + 576} - 20875 \log {\left (x + \frac {3}{5} \right )} + 20875 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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