integration (1 Viewer)

[martin310015]

how do u integrate cot^2(x) and 1/(-x^2+4x-3)^1/2...thanx

 

[wogboy]

how do u integrate cot^2(x)

I cot^2(x) dx
= I cosec^2(x) - 1 dx
= I sec^2(x - pi/2) - 1 dx
= tan(x - pi/2) - x + C
= - cot(x) - x + C

and 1/(-x^2+4x-3)^1/2...thanx

Start off by completing the square in the denominator:

I 1/sqrt(-x^2 + 4x - 3) dx
= I 1/sqrt(-x^2 + 4x - 4 + 1) dx
= I 1/(sqrt(1 - (x-2)^2) dx
= arcsin(x-2) + C