the function f is defined by f(x) = (2/(x^2 −1)) a) Express f into partial fraction b.show that ∫


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Question Number 75098 by Rio Michael last updated on 07/Dec/19
$the function f is defined by f(x) = (2/(x^2 −1)) a) Express f into partial fraction b.show that ∫_3 ^5 f(x) dx = ln((4/3))$
$the function f is defined by f (x) = \frac{2}{x^{2} - 1}$ $a) Express f into partial fraction$ $b . show that \int_{3}^{5} f (x) d x = l n (\frac{4}{3})$
	Answered by peter frank last updated on 07/Dec/19

	$y = \frac{2}{(x - 1) (x + 1)}$ $2 = \frac{A}{x - 1} + \frac{B}{x + 1}$ $2 = A (x + 1) + B (x - 1)$ $A = 1 B = - 1$ $y = \int (\frac{1}{x - 1} - \frac{1}{x + 1}) d y$ $Missing \left or extra \right$ $y^{^{'}} = l n (\frac{2}{3}) - l n (\frac{1}{2}) = l n (\frac{4}{3})$
	Commented by Rio Michael last updated on 07/Dec/19

	$t h a n k s s i r$
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