Optimal. Leaf size=81 \[ \frac {6875}{3 x+2}+\frac {1375}{2 (3 x+2)^2}+\frac {275}{3 (3 x+2)^3}+\frac {55}{4 (3 x+2)^4}+\frac {11}{5 (3 x+2)^5}+\frac {7}{18 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 81, 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} \[ \frac {6875}{3 x+2}+\frac {1375}{2 (3 x+2)^2}+\frac {275}{3 (3 x+2)^3}+\frac {55}{4 (3 x+2)^4}+\frac {11}{5 (3 x+2)^5}+\frac {7}{18 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^7 (3+5 x)} \, dx &=\int \left (-\frac {7}{(2+3 x)^7}-\frac {33}{(2+3 x)^6}-\frac {165}{(2+3 x)^5}-\frac {825}{(2+3 x)^4}-\frac {4125}{(2+3 x)^3}-\frac {20625}{(2+3 x)^2}-\frac {103125}{2+3 x}+\frac {171875}{3+5 x}\right ) \, dx\\ &=\frac {7}{18 (2+3 x)^6}+\frac {11}{5 (2+3 x)^5}+\frac {55}{4 (2+3 x)^4}+\frac {275}{3 (2+3 x)^3}+\frac {1375}{2 (2+3 x)^2}+\frac {6875}{2+3 x}-34375 \log (2+3 x)+34375 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.08, size = 75, normalized size = 0.93 \[ \frac {1237500 (3 x+2)^5+123750 (3 x+2)^4+16500 (3 x+2)^3+2475 (3 x+2)^2+396 (3 x+2)+70}{180 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 135, normalized size = 1.67 \[ \frac {300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 6187500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 6187500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 309504888 \, x + 41722762}{180 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 53, normalized size = 0.65 \[ \frac {300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 309504888 \, x + 41722762}{180 \, {\left (3 \, x + 2\right )}^{6}} + 34375 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 34375 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.89 \[ -34375 \ln \left (3 x +2\right )+34375 \ln \left (5 x +3\right )+\frac {7}{18 \left (3 x +2\right )^{6}}+\frac {11}{5 \left (3 x +2\right )^{5}}+\frac {55}{4 \left (3 x +2\right )^{4}}+\frac {275}{3 \left (3 x +2\right )^{3}}+\frac {1375}{2 \left (3 x +2\right )^{2}}+\frac {6875}{3 x +2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 76, normalized size = 0.94 \[ \frac {300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 309504888 \, x + 41722762}{180 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 34375 \, \log \left (5 \, x + 3\right ) - 34375 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 65, normalized size = 0.80 \[ \frac {\frac {6875\,x^5}{3}+\frac {138875\,x^4}{18}+\frac {841775\,x^3}{81}+\frac {756085\,x^2}{108}+\frac {955262\,x}{405}+\frac {20861381}{65610}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}}-68750\,\mathrm {atanh}\left (30\,x+19\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 73, normalized size = 0.90 \[ - \frac {- 300712500 x^{5} - 1012398750 x^{4} - 1363675500 x^{3} - 918643275 x^{2} - 309504888 x - 41722762}{131220 x^{6} + 524880 x^{5} + 874800 x^{4} + 777600 x^{3} + 388800 x^{2} + 103680 x + 11520} + 34375 \log {\left (x + \frac {3}{5} \right )} - 34375 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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