What is the antiderivative of f(x)=x*e^4x.

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We need to find the antiderivative of f(x)=x*e^4x

We solve this problem using Integration by parts:

Int [f(x)g'(x) dx = f(x)g(x)- Int [ f'(x)g(x) dx]

Let f(x) = x and g'(x)= e^4x

=> g(x) = e^4x/4

Int [ x*e^4x dx] = x*e^4x / 4 - Int [ e^4x/4 dx]

=> x* e^4x/4 - e^4x / 16 + C

Therefore the antiderivative of f(x)=x*e^4x is x*e^4x/4 - e^4x /16 + C

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