Question

450 sau 451 cineva??? Multumesc!!!!

Answer 1

Este scrisa mai pe scurt rezolvarea, sper sa o intelegi.

$\\ \int ^{\frac{\Pi }{2}}_0\:\frac{dx}{2cosx+3} => \\ \\ =\int \frac{2}{u^2+5}du \\ \\ =2\cdot \int \:\frac{1}{u^2+5}du \\ \\=2\cdot \frac{1}{\sqrt{5}}\cdot \int \:\frac{1}{v^2+1}dv \\ \\ =2\cdot \frac{1}{\sqrt{5}}\arctan \left(v\right) \\ \\ =2\cdot \frac{1}{\sqrt{5}}\arctan \left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{5}}\right) \\ =\frac{2}{\sqrt{5}}\arctan \left(\frac{1}{\sqrt{5}}\right)-0 \\ \\ \boxed{=\frac{2}{\sqrt{5}}\arctan \left(\frac{1}{\sqrt{5}}\right)}$