The antiderivative of f(x)=x*e^8x can be found using integration by parts.

Int [u dv ]= u*v - Int[ v du]

Let u = x => du = 1

dv = e^8x => v = e^8x/8

Int [ x*e^8x ] = (x*e^8x)/8 - Int [1*(e^8x)/8]

=> (x*e^8x)/8 - (e^8x)/64

**The anti-derivative is (x*e^8x)/8 - (e^8x)/64 + C**

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