The integral d x a x+b x is of the form 1 r In [ ( x+ 2 ) ] . What is r equal to?

Step-by-step solution

Given that, dx a x + b x = 1 r [ ( x + 2 ) ] Let a = r , b = r aligned & d x r x+r x = 1 r 1 (x+ ) & = 1 r cosec (x+ ) d x= 1 r [ ( x+ 2 ) ] aligned aligned & a=r a^2=r^2 ^2 ...(i) & b=r b^2=r^2 ^2 ...(ii) aligned Adding (i) and (ii), we get aligned r ^2 & = a ^2+ b ^2 r & = a ^2+ b ^2 . aligned