If a>0 , then _ - ^ ^2 x 1+a^x d x is equal to

Step-by-step solution

Let l= _ - ^ ^2 x 1+a^x d x Put x=-x , we get aligned & I=- _ ^ - ^2(-x) 1+a^ -x d x & I= _ - ^ a^x ^2 x 1+a^x d x aligned On adding Fqs. (i) and (ii), we get aligned 2 I & = _ - ^ (1+a^x ) ^2 x (1+a^x ) d x & = _ - ^ ^2 x d x & =2 ₀^ ^2 x d x= ₀^ (1- 2 x) d x & = [x+ 2 x 2 ]₀^ & = ( + 2 2 -0-0 ) 2 I & = I & = 2 aligned