Tích phân

T

trantien.hocmai

$$I=\int_0^{\dfrac{\pi}{2}} \dfrac{\cos 2x}{(\sin x-\cos x+2)^3}dx \\
=\int_0^{\dfrac{\pi}{2}} \dfrac{(\cos x-\sin x)(\sin x+\cos x)dx}{(\sin x-\cos x+2)^3}dx \\$$
$\text{đặt u}=\sin x-\cos x \rightarrow du=(\cos x+\sin x)dx \\
\text{ta có} \\$
$$I=\int \dfrac{-udu}{(u+2)^3} \\$$
 
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