Homework Soursethe cosarc cot x is costheta xsq trx21 but the formula for
the cos(arc cot x) is cos(theta) = (x)/sq tr(x^2+1) but the formula for arc cot is -u\'/1+u^2
the answer i got using the formula was (-1)/sq rt(x^2+1)
where did I go wrong?
How am I misusing the formula?
the answer i got using the formula was (-1)/sq rt(x^2+1)
where did I go wrong?
How am I misusing the formula?
Solution
cos(arc cotx) = cos(arc cos(x/x^2+1))
= x/(x^2+1)
I = integral of x/(x^2+1)
I = 1/2 integral of 2x/(x^2+1)
let x^2+1 = t
2xdx = dt
I = 1/2 integral of t^-1/2
I = 1/2 *2t^1/2 + C
I = t^1/2 + C
I = x^2+1
