0-pi-2-dx-1-tan-2023-x-

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!