Integrate 1/(x(x^2+1)) dx

Question

using trig substitution

Answer 1

let x = tan t
then dx = sec^2 t dt

sec^2 t dt/[ tan t (1+tan^2 t) ]

NOTE: 1+tan^2 t = sec^2 t !!! wow that helps :)

so we have
dt/tan t = ctn t dt

= ln (sin u)