Need Help With Integrals!!!?

Question

I can't solve these problems and i'm desperate right now.
Integral of sqrt(9-x^2)
Integral of Tan inverse
Integral of sqrt(tanx)sec^2
Integral of Cos2X
Integral of SecX

if you could help me with anyone of these, it would be greatly appreciated.

Answer 1

Let me give you some hints for starters:
1). Let x = 3 sin t, dx = 3 cos t dt.
The integral reduces to ∫ 9cos² t dt.
Now cos² t = (1+ cos 2t)/2. The rest is easy.

2. Use integration by parts:
u = arctan x dv = dx
du = dx/(1 + x²) v = x.
Now put it together!

3. Let u = tan x du =sec²x dx

4. Let u = 2x and integrate cos u du/2.

5. Standard trick: Multiply sec x by (sec x + tan x)/(sec x + tan x)
What is the relationship between numerator and denominator?

Hope that's enough to get you started.
If you need more help, feel free to e-mail me.
Good luck!