Optimal. Leaf size=90 \[ -\frac {125000}{3 x+2}-\frac {34375}{5 x+3}-\frac {20875}{2 (3 x+2)^2}-\frac {3350}{3 (3 x+2)^3}-\frac {505}{4 (3 x+2)^4}-\frac {68}{5 (3 x+2)^5}-\frac {7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (5 x+3) \]
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Rubi [A] time = 0.04, antiderivative size = 90, 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} \[ -\frac {125000}{3 x+2}-\frac {34375}{5 x+3}-\frac {20875}{2 (3 x+2)^2}-\frac {3350}{3 (3 x+2)^3}-\frac {505}{4 (3 x+2)^4}-\frac {68}{5 (3 x+2)^5}-\frac {7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (5 x+3) \]
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)^2} \, dx &=\int \left (\frac {21}{(2+3 x)^7}+\frac {204}{(2+3 x)^6}+\frac {1515}{(2+3 x)^5}+\frac {10050}{(2+3 x)^4}+\frac {62625}{(2+3 x)^3}+\frac {375000}{(2+3 x)^2}+\frac {2184375}{2+3 x}+\frac {171875}{(3+5 x)^2}-\frac {3640625}{3+5 x}\right ) \, dx\\ &=-\frac {7}{6 (2+3 x)^6}-\frac {68}{5 (2+3 x)^5}-\frac {505}{4 (2+3 x)^4}-\frac {3350}{3 (2+3 x)^3}-\frac {20875}{2 (2+3 x)^2}-\frac {125000}{2+3 x}-\frac {34375}{3+5 x}+728125 \log (2+3 x)-728125 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.06, size = 92, normalized size = 1.02 \[ -\frac {125000}{3 x+2}-\frac {34375}{5 x+3}-\frac {20875}{2 (3 x+2)^2}-\frac {3350}{3 (3 x+2)^3}-\frac {505}{4 (3 x+2)^4}-\frac {68}{5 (3 x+2)^5}-\frac {7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 155, normalized size = 1.72 \[ -\frac {3538687500 \, x^{6} + 14036793750 \, x^{5} + 23195441250 \, x^{4} + 20438672625 \, x^{3} + 10128331755 \, x^{2} + 14562500 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 14562500 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 2676272018 \, x + 294588002}{20 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 85, normalized size = 0.94 \[ -\frac {34375}{5 \, x + 3} + \frac {5625 \, {\left (\frac {1100034}{5 \, x + 3} + \frac {811665}{{\left (5 \, x + 3\right )}^{2}} + \frac {304700}{{\left (5 \, x + 3\right )}^{3}} + \frac {58650}{{\left (5 \, x + 3\right )}^{4}} + \frac {4700}{{\left (5 \, x + 3\right )}^{5}} + 604017\right )}}{4 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{6}} + 728125 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 81, normalized size = 0.90 \[ 728125 \ln \left (3 x +2\right )-728125 \ln \left (5 x +3\right )-\frac {7}{6 \left (3 x +2\right )^{6}}-\frac {68}{5 \left (3 x +2\right )^{5}}-\frac {505}{4 \left (3 x +2\right )^{4}}-\frac {3350}{3 \left (3 x +2\right )^{3}}-\frac {20875}{2 \left (3 x +2\right )^{2}}-\frac {125000}{3 x +2}-\frac {34375}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 86, normalized size = 0.96 \[ -\frac {3538687500 \, x^{6} + 14036793750 \, x^{5} + 23195441250 \, x^{4} + 20438672625 \, x^{3} + 10128331755 \, x^{2} + 2676272018 \, x + 294588002}{20 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 728125 \, \log \left (5 \, x + 3\right ) + 728125 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 76, normalized size = 0.84 \[ 1456250\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {145625\,x^6}{3}+\frac {3465875\,x^5}{18}+\frac {51545425\,x^4}{162}+\frac {30279515\,x^3}{108}+\frac {225074039\,x^2}{1620}+\frac {1338136009\,x}{36450}+\frac {147294001}{36450}}{x^7+\frac {23\,x^6}{5}+\frac {136\,x^5}{15}+\frac {268\,x^4}{27}+\frac {176\,x^3}{27}+\frac {208\,x^2}{81}+\frac {2048\,x}{3645}+\frac {64}{1215}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 82, normalized size = 0.91 \[ - \frac {3538687500 x^{6} + 14036793750 x^{5} + 23195441250 x^{4} + 20438672625 x^{3} + 10128331755 x^{2} + 2676272018 x + 294588002}{72900 x^{7} + 335340 x^{6} + 660960 x^{5} + 723600 x^{4} + 475200 x^{3} + 187200 x^{2} + 40960 x + 3840} - 728125 \log {\left (x + \frac {3}{5} \right )} + 728125 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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