₀^ x d x 1+ x ,(0 < < ) is equal to

Step-by-step solution

array l Let I= ₀^ x d x 1+ x .. I= ₀^ ( -x) 1+ ( -x) d x array On adding Eqs. (i) and (ii), we get aligned 2 I= ₀^ d x 1+ x = ₀^ d x 1+ ( 2 x / 2 1+ ² x / 2 ) = ₀^ ² x / 2 d x (1+ ² x / 2 )+ (2 x / 2) aligned Put x / 2=t (1 / 2) ² x / 2 d x=d t array l 2 I= ₀^ 2 d t 1+t²+2 t I= ₀^ d t 1+t²+2 t = ₀^ d t (t+ )²+ ² = [ ⁻¹ ( t+ ) ]₀^ I= array