We want to compute the integral
\int tan^(-1)(x)dx
. If we use integration by parts, with
u=tan^(-1)(x)
and
dv=dx
, what do we get?
tan^(-1)(x)-\int x*tan^(-1)(x)dx
x*tan^(-1)(x)-\int (1)/(1 x^(2))dx
x*tan^(-1)(x)-\int (x)/(1 x^(2))dx
(x)/(1 x^(2))-\int (1)/(1 x^(2))dx