∫{((x^2 −x−21)/(2x^3 −x^2 +8x−4))}dx


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Question Number 158176 by Odhiambojr last updated on 31/Oct/21
$∫{((x^2 −x−21)/(2x^3 −x^2 +8x−4))}dx$
$\int {\frac{x^{2} - x - 21}{2 x^{3} - x^{2} + 8 x - 4}} d x$
	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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