integrate sin(x)/(1+cos^2(x))?

Answer 1

You have to use substitution.

Let u = cos(x)
du = -sin(x) dx, so
-du = sin(x)dx

Therefore, your new integral becomes:

-1 / (1 + u^2)

And integrating that, you get
- tan(inverse) (u)

Resubstituting u=cos(x), you get

-tan(inverse) (cos(x))

Answer 2

first off you should know that
sin^2(x) + cos^2(x) = 1
(it's a pythagorean identity)
so you can say that
cos^2(x) = 1 - sin^2(x)

substitute this in for cos^2(x)

sinx/(1 + cos^2(x))
sinx/(1 + (1 - sin^2(x))
sinx/(2 - sin^2(x))
this is a far as you can go so the answer is

sinx/(2 - sin^2(x))

Answer 3

cos(x)/2sin(x) ????????

I know I shouldn't be shooting from the hip on this one - been a long time since college.

Answer 4

-arctan(cos(x)


Doug