If d x [3] ¹¹ x x =- ( 3 8 f (x)+ 3 2 ~g (x) )+ c then

Step-by-step solution

Let aligned I & = d x [3] ¹¹ x x & = d x ^ 11 3 x ^ 1 3 x & = ^4 x ^ 11 3 x ~d x aligned ... [Dividing numerator and denominator by . ^ 11 3 x ]= (1+ ^2 x ) ^2 x ^ 11 3 x ~d x aligned & Let x=t & ^2 x d x=d t & = (1+t^2 ) d t t^ 11 3 & = t^ - 11 3 d t+ t^ -5 3 d t aligned aligned & = -3 8 t ^ -8 3 - 3 2 t ^ -2 3 + c & =- [ 3 8 t ^ -8 3 + 3 2 t ^ -2 3 ]+ c & =- [ 3 8 ^ -8 3 x+ 3 2 ^ -2 3 x ]+ c f (x) & = ^ -8 3 x, ~g (x)= ^ -2 3 x aligned