Question

test for convergence
integrate (0 to pi/2) cotx dx

Answer 1

integral by sub..
int (cot(x)) dx = int (cos(x)/sin(x)) dx
let u=sin(x)
du=cos(x) dx, so the integration can be
int (1/u) du = ln(u)
subtitute back that u=sin(x)
= ln(sin(x))
now, just calculate for limits integral from 0 to pi/2