∫((2sin x+3cos x)/(7sin x−2cos x))


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Question Number 20388 by tammi last updated on 26/Aug/17

$\int \frac{2 \sin x + 3 \cos x}{7 \sin x - 2 \cos x}$
	Answered by $@ty@m last updated on 26/Aug/17

	$L e t 2 s i n x + 3 c o s x = A (7 s i n x - 2 c o s x) + B (7 c o s x + 2 s i n x)$ $\Rightarrow 7 A - 2 B = 2$ $- 2 A + 7 B = 3$ $\Rightarrow A = \frac{4}{9}, B = \frac{5}{9}$ $∴ I = \frac{4}{9} \int d x + \frac{5}{9} \int \frac{d t}{t} w h e r e t = 7 s i n x - 2 c o s x$ $I = \frac{4}{9} x + \frac{5}{9} l n (7 s i n x - 2 c o s x) + C$
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