Integral ln(arctgx)/1+x^2*dx

Question

Integral ln(arctgx)/1+x^2*dx

Answer 1

∫(2^arctg(x)/(1+x²))dx=
Замена t=arctgx  =>  dt=dx/(1+x²)
=∫2^tdt=2^t/ln2+C=2^(arctgx)/ln2+C.
∫(2х²/(1+x²))dx=2∫((х²+1-1)/(1+x²))dx=2∫(1-1/(1+x²))dx=2x-2arctgx+C.