Integrating sqrt(3-x²)/sqrt(3) and sqrt(3-3x²)

[ACLerok]

how do i integrate sqrt(3-(x^2))/sqrt(3)? i put the sqrt(3) outside the integral and tried using the substitution method to integrate it but there is still an x in there?

same thing with integrating sqrt(3-3*(x^2))

Thanks! This thing is due tomorrow..

 

[vsage]

that's a classic trig substitution case. (Use sine trig substitution).

 

[ACLerok]

that's a classic trig substitution case. (Use sine trig substitution).

both of them?

 

[vsage]

Yeah it's not that much different with both.. just different coefficients you have to pull out of the square root.

 

[ACLerok]

alright i think i almost got it.. now i have another question, what's the integral of cos^2(x)?

 

[arildno]

You've got the identity:
$$\cos^{2}x=\frac{1+\cos2x}{2}$$