Thread: integral (0 to pi/2) cosx/sqrt(1+sin^2x) help?

I stumbled upon this question in my text book,
could someone help me solve it?

integral (0 to pi/2) cosx/sqrt(1+sin^2x)

So the problem is ?

Let u= sin(x) so that du= cos(x)dx. When x=0, u= 0 and when , u= 1 so the problem becomes .

Now, use a trig substitution to do that- remembering that .

Since I am first getting rid of trig functions, and then introducing trig functions, you could probably do this with a single trig identity, but that is how I would handle it.