What is e^ x x ^3 x- x ^2 x d x equal to?

Step-by-step solution

Let us differentiate all the options one by one to get the expression in the question whose integral is to be found. Here x e^ x is the common term in all the options. So, let us differentiate it first. aligned & Let l=x e^ x & d l d x =e^ x [x x+1] & d l d x = e^ x ^2 x [x ^3 x+ ^2 x ] aligned Let m= x e^ x aligned & d m d x = x e^ x x+e^ x x x & d m d x =e^ x [1+ x ^2 x ] & d m d x = e^ x ^2 x [ ^2 x+ x ] aligned Differentiation of option (a) is aligned & = e^ x ^2 x [x ^3 x+ ^2 x+ ^2 x+ x ] & = e^ x ^2 x [x ^3 x