_ - / 4 ^ / 4 ⁻⁸ x d x=

Step-by-step solution

I= _ - / 4 ^ / 4 1 ^8 x d x= _ - / 4 ^ / 4 ( ^6 x ) ( ^2 x ) d x On putting x=t ^2 x d x=d t aligned I & = _ -1 ^1 (t^2+1 )^3 d t= _ -1 ^1 (t^6+3 t^4+3 t^2+1 ) d t & =2 ₀^1 (t^6+3 t^4+3 t^2+1 ) d t & =2 [ t^7 7 + 3 t^5 5 +t^3+t ]₀^1=2 [ 1 7 + 3 5 +2 ] & = 192 35 aligned