use the technique of integration by parts to evaluate ∫ x^(4) e^(3x) dx.
I = ∫ x^(4) e^(3x) dx = (1/3).x^4.e^(3x) - (1/3) ∫ 4x^3.e^(3x) dx
= (1/3).x^4.e^(3x) - (1/3){(4/3)x^3.e^(3x) - (4) ∫ x^2.e^(3x) dx}
= (1/3).x^4.e^(3x) - (1/3){(4/3)x^3.e^(3x) - (4)[(1/3)x^2.e^(3x) - (2/3) ∫ x.e^(3x) dx]}
= (1/3).x^4.e^(3x) - (1/3){(4/3)x^3.e^(3x) - (4)[(1/3)x^2.e^(3x) - (2/3)((1/3)x.e^(3x) - (1/9e^(3x))]}
= {(1/3).x^4 - (1/3){(4/3)x^3 - (4)[(1/3)x^2 - (2/9)x + (2/27)]}}.e^(3x)
= {(1/3).x^4 - (1/3){(4/3)x^3 - (4/3)x^2 + (8/9)x - (8/27)}}.e^(3x)
= {(1/3).x^4 - (4/9)x^3 + (4/9)x^2 - (8/27)x + (8/81)}.e^(3x)
=81{27.x^4 - 36.x^3 + 36.x^2 - 24x + 8}.e^(3x)