Замена переменной:
x+1=t
x=t-1
dx=dt
пределы
при x=-1, получим t=0
при x=1, получим t=2
= ∫ ^(2)_(0)(t-2)dt/(t^2+2^2)=(1/2) ∫ ^(2)_(0)(2tdt)/(t^2+4-2∫ ^(2)_(0)dt/(t^2+2^2)=
=(1/2)*ln|t^2+4|^(2)_(0)- 2*(1/2)arctg(t/2)|^(2)_(0)=
=(1/2)*ln8-(1/2)*ln4-arctg1=(1/2)ln(8/4)-(π/4)=[b](1/2)ln2-(π/4)[/b]