∫_0 ^(π/2) (dx/(1+tan^(2023) x))=???????


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Question Number 200464 by Frix last updated on 19/Nov/23

$\underset{0}{\int^{\frac{π}{2}}} \frac{d x}{1 + \tan^{2023} x} = ? ? ? ? ? ? ?$
	Answered by som(math1967) last updated on 19/Nov/23

	$I = \underset{0}{\int^{\frac{π}{2}}} \frac{{c o s}^{2023} x d x}{{s i n}^{2023} x + {c o s}^{2023} x}$ $2 I = \underset{0}{\int^{\frac{π}{2}}} \frac{{c o s}^{2023} (\frac{π}{2} - x) + {c o s}^{2023} x d x}{{s i n}^{2023} (\frac{π}{2} - x) + {c o s}^{2023} (\frac{π}{2} - x)}$ $2 I = {[x]}_{0}^{\frac{π}{2}} \Rightarrow I = \frac{π}{4}$
	Commented by Frix last updated on 21/Nov/23
	Yes! Thank you!
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