x-2-x-21-2x-3-x-2-8x-4-dx-

Question Number 158176 by Odhiambojr last updated on 31/Oct/21

\int {\frac{x^{2} - x - 21}{2 x^{3} - x^{2} + 8 x - 4}} d x

Answered by MJS_new last updated on 31/Oct/21

= \int \frac{x^{2} - x - 21}{(2 x - 1) (x^{2} + 4)} d x =

= \int (\frac{3 x}{x^{2} + 4} - \frac{5}{2 x - 1} + \frac{1}{x^{2} + 4}) d x =

= \frac{3}{2} \ln (x^{2} + 4) - \frac{5}{2} \ln ∣ 2 x - 1 ∣ + \frac{1}{2} \arctan \frac{x}{2} + C

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