could someone show me the steps in between the first two bol

could someone show me the steps in between the first two bold parts

Possible intermediate steps: For the integrand substitute x = 2tan(u) and dx = 2 sec2(u)du, Then Factor out constants: The integral of cot(u)csc(u) is -csc(u): Substitute back for u = tan-1(x/2):

Solution

in that first he had taken x=2tanu so
dx=2sec²u so (x²+4)=(4tan²u+4)=4(tan²u+1) we know that sec²u-tan²u=1

s0 4sec²u=4(tan²u+1)

so (4tan²u+4)=   ( 4sec²u)

=2secu and we know that x=2tanu

t=an^-1(x/2) =u

so here du=1/(1+x²/4)(1/2)dx=2/4+x² substituting all of these

=1/4tan²u(1/(4+x²))2/4+x²⁼