Optimal. Leaf size=110 \[ \frac {43848750}{3 x+2}+\frac {20418750}{5 x+3}+\frac {6618975}{2 (3 x+2)^2}-\frac {831875}{2 (5 x+3)^2}+\frac {317845}{(3 x+2)^3}+\frac {64317}{2 (3 x+2)^4}+\frac {15708}{5 (3 x+2)^5}+\frac {539}{2 (3 x+2)^6}+\frac {49}{3 (3 x+2)^7}-280500000 \log (3 x+2)+280500000 \log (5 x+3) \]
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Rubi [A] time = 0.06, antiderivative size = 110, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {43848750}{3 x+2}+\frac {20418750}{5 x+3}+\frac {6618975}{2 (3 x+2)^2}-\frac {831875}{2 (5 x+3)^2}+\frac {317845}{(3 x+2)^3}+\frac {64317}{2 (3 x+2)^4}+\frac {15708}{5 (3 x+2)^5}+\frac {539}{2 (3 x+2)^6}+\frac {49}{3 (3 x+2)^7}-280500000 \log (3 x+2)+280500000 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^8 (3+5 x)^3} \, dx &=\int \left (-\frac {343}{(2+3 x)^8}-\frac {4851}{(2+3 x)^7}-\frac {47124}{(2+3 x)^6}-\frac {385902}{(2+3 x)^5}-\frac {2860605}{(2+3 x)^4}-\frac {19856925}{(2+3 x)^3}-\frac {131546250}{(2+3 x)^2}-\frac {841500000}{2+3 x}+\frac {4159375}{(3+5 x)^3}-\frac {102093750}{(3+5 x)^2}+\frac {1402500000}{3+5 x}\right ) \, dx\\ &=\frac {49}{3 (2+3 x)^7}+\frac {539}{2 (2+3 x)^6}+\frac {15708}{5 (2+3 x)^5}+\frac {64317}{2 (2+3 x)^4}+\frac {317845}{(2+3 x)^3}+\frac {6618975}{2 (2+3 x)^2}+\frac {43848750}{2+3 x}-\frac {831875}{2 (3+5 x)^2}+\frac {20418750}{3+5 x}-280500000 \log (2+3 x)+280500000 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.16, size = 112, normalized size = 1.02 \[ \frac {43848750}{3 x+2}+\frac {20418750}{5 x+3}+\frac {6618975}{2 (3 x+2)^2}-\frac {831875}{2 (5 x+3)^2}+\frac {317845}{(3 x+2)^3}+\frac {64317}{2 (3 x+2)^4}+\frac {15708}{5 (3 x+2)^5}+\frac {539}{2 (3 x+2)^6}+\frac {49}{3 (3 x+2)^7}-280500000 \log (5 (3 x+2))+280500000 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 195, normalized size = 1.77 \[ \frac {30672675000000 \, x^{8} + 160520332500000 \, x^{7} + 367435926000000 \, x^{6} + 480493891350000 \, x^{5} + 392612784696000 \, x^{4} + 205262100529200 \, x^{3} + 67053019228048 \, x^{2} + 8415000000 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (5 \, x + 3\right ) - 8415000000 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (3 \, x + 2\right ) + 12513316868859 \, x + 1021373267628}{30 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 75, normalized size = 0.68 \[ \frac {30672675000000 \, x^{8} + 160520332500000 \, x^{7} + 367435926000000 \, x^{6} + 480493891350000 \, x^{5} + 392612784696000 \, x^{4} + 205262100529200 \, x^{3} + 67053019228048 \, x^{2} + 12513316868859 \, x + 1021373267628}{30 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{7}} + 280500000 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 280500000 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 99, normalized size = 0.90 \[ -280500000 \ln \left (3 x +2\right )+280500000 \ln \left (5 x +3\right )+\frac {49}{3 \left (3 x +2\right )^{7}}+\frac {539}{2 \left (3 x +2\right )^{6}}+\frac {15708}{5 \left (3 x +2\right )^{5}}+\frac {64317}{2 \left (3 x +2\right )^{4}}+\frac {317845}{\left (3 x +2\right )^{3}}+\frac {6618975}{2 \left (3 x +2\right )^{2}}+\frac {43848750}{3 x +2}-\frac {831875}{2 \left (5 x +3\right )^{2}}+\frac {20418750}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 106, normalized size = 0.96 \[ \frac {30672675000000 \, x^{8} + 160520332500000 \, x^{7} + 367435926000000 \, x^{6} + 480493891350000 \, x^{5} + 392612784696000 \, x^{4} + 205262100529200 \, x^{3} + 67053019228048 \, x^{2} + 12513316868859 \, x + 1021373267628}{30 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} + 280500000 \, \log \left (5 \, x + 3\right ) - 280500000 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 95, normalized size = 0.86 \[ \frac {18700000\,x^8+\frac {293590000\,x^7}{3}+\frac {6048328000\,x^6}{27}+\frac {23728093400\,x^5}{81}+\frac {6462761888\,x^4}{27}+\frac {152046000392\,x^3}{1215}+\frac {33526509614024\,x^2}{820125}+\frac {4171105622953\,x}{546750}+\frac {170228877938}{273375}}{x^9+\frac {88\,x^8}{15}+\frac {1147\,x^7}{75}+\frac {15694\,x^6}{675}+\frac {46004\,x^5}{2025}+\frac {5992\,x^4}{405}+\frac {23408\,x^3}{3645}+\frac {97952\,x^2}{54675}+\frac {5312\,x}{18225}+\frac {128}{6075}}-561000000\,\mathrm {atanh}\left (30\,x+19\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 104, normalized size = 0.95 \[ - \frac {- 30672675000000 x^{8} - 160520332500000 x^{7} - 367435926000000 x^{6} - 480493891350000 x^{5} - 392612784696000 x^{4} - 205262100529200 x^{3} - 67053019228048 x^{2} - 12513316868859 x - 1021373267628}{1640250 x^{9} + 9622800 x^{8} + 25084890 x^{7} + 38136420 x^{6} + 37263240 x^{5} + 24267600 x^{4} + 10533600 x^{3} + 2938560 x^{2} + 478080 x + 34560} + 280500000 \log {\left (x + \frac {3}{5} \right )} - 280500000 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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