# Integration 0 to infinity (x^4 e^-2ax dx)

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You should evaluate the improper integral such that:

int_0^(oo)x^4*e^(-2ax) dx = lim_(n->oo) int_0^n x^4*e^(-2ax) dx

You need to use integration by parts such that:

int udv = uv - int vdu

u = x^4 => du = 4x^3dx

dv = e^(-2ax) dx => v = (e^(-2ax))/(-2a)

int x^4*e^(-2ax) dx = (x^4*e^(-2ax))/(-2a) + int 4x^3(e^(-2ax))/(2a) dx

int x^4*e^(-2ax) dx = (x^4*e^(-2ax))/(-2a)+ (2/a)int x^3(e^(-2ax)) dx

You need to use integration by parts to evaluate int x^3(e^(-2ax)) dx   such that:

u =x^3 => du = 3x^2 dx

dv = e^(-2ax) dx => v = (e^(-2ax))/(-2a)

int x^3(e^(-2ax)) dx = (x^3*e^(-2ax))/(-2a) + int 3x^2(e^(-2ax))/(2a) dx

int x^3(e^(-2ax)) dx = (x^3*e^(-2ax))/(-2a) + (3/2a) int x^2(e^(-2ax)) dx

You need to use integration by parts to evaluate int x^2(e^(-2ax)) dx  such that:

u = x^2 => du = 2x dx

`dv =...

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