`underset(0)overset(oo)int (log x)/(1+x^(2))dx`

Evaluate the following integrals: underset(0)overset(1)int(log(1+x))/(1+x^2) dx

If I_(1)=int_(0)^(oo) (dx)/(1+x^(4))dx and I_(2)=underset(0)overset(oo)int x^(2)(dx)/(1+x^(4))"then"n (I_(1))/(I_(2))=

Evaluate: underset0overset1 int (log(1+x))/(1+x^2)dx

underset(1)overset(e )int log x dx =

Evaluate the following integrals : underset(0)overset(1)int(2x-1)/(1+x-x^2)dx

underset0overset1int xlog(1+2x)dx

Evaluate: underset(0)overset(1)int(1/(1+x))dx .

underset0overset1int (2x)/((x^2+1)(x^2+2))dx

Evaluate underset(-1)overset(1)int log((x^2+x+1)/(x^2-x+1))dx .

Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2 .