[Toán 12] Tính nguyên hàm, tích phân

V

vivietnam

$I=-\int \dfrac{2cosx+1}{\sqrt{1+3cosx}}d(cosx)$
Đặt $\sqrt{1+3cosx}=t \Longrightarrow d(cosx)=\dfrac{2}{3}tdt$
$I=-\int \dfrac{\dfrac{2}{3}(t^2-1)+1}{t}.\dfrac{2}{3}tdt$
$I=-\int (\dfrac{4}{9}t^2+\dfrac{2}{9})dt=-\dfrac{4t^3}{27}-\dfrac{2t}{9}$
 
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