Optimal. Leaf size=70 \[ \frac {1375}{3 x+2}+\frac {275}{2 (3 x+2)^2}+\frac {55}{3 (3 x+2)^3}+\frac {11}{4 (3 x+2)^4}+\frac {7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 70, 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} \begin {gather*} \frac {1375}{3 x+2}+\frac {275}{2 (3 x+2)^2}+\frac {55}{3 (3 x+2)^3}+\frac {11}{4 (3 x+2)^4}+\frac {7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx &=\int \left (-\frac {7}{(2+3 x)^6}-\frac {33}{(2+3 x)^5}-\frac {165}{(2+3 x)^4}-\frac {825}{(2+3 x)^3}-\frac {4125}{(2+3 x)^2}-\frac {20625}{2+3 x}+\frac {34375}{3+5 x}\right ) \, dx\\ &=\frac {7}{15 (2+3 x)^5}+\frac {11}{4 (2+3 x)^4}+\frac {55}{3 (2+3 x)^3}+\frac {275}{2 (2+3 x)^2}+\frac {1375}{2+3 x}-6875 \log (2+3 x)+6875 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 50, normalized size = 0.71 \begin {gather*} \frac {2227500 x^4+6014250 x^3+6091800 x^2+2743565 x+463586}{20 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (-3 (5 x+3)) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.49, size = 115, normalized size = 1.64 \begin {gather*} \frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 137500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 137500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 2743565 \, x + 463586}{20 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 48, normalized size = 0.69 \begin {gather*} \frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \, {\left (3 \, x + 2\right )}^{5}} + 6875 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6875 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 63, normalized size = 0.90 \begin {gather*} -6875 \ln \left (3 x +2\right )+6875 \ln \left (5 x +3\right )+\frac {7}{15 \left (3 x +2\right )^{5}}+\frac {11}{4 \left (3 x +2\right )^{4}}+\frac {55}{3 \left (3 x +2\right )^{3}}+\frac {275}{2 \left (3 x +2\right )^{2}}+\frac {1375}{3 x +2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 66, normalized size = 0.94 \begin {gather*} \frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 6875 \, \log \left (5 \, x + 3\right ) - 6875 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 55, normalized size = 0.79 \begin {gather*} \frac {\frac {1375\,x^4}{3}+\frac {2475\,x^3}{2}+\frac {101530\,x^2}{81}+\frac {548713\,x}{972}+\frac {231793}{2430}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}}-13750\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 63, normalized size = 0.90 \begin {gather*} - \frac {- 2227500 x^{4} - 6014250 x^{3} - 6091800 x^{2} - 2743565 x - 463586}{4860 x^{5} + 16200 x^{4} + 21600 x^{3} + 14400 x^{2} + 4800 x + 640} + 6875 \log {\left (x + \frac {3}{5} \right )} - 6875 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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