calculus help

i am getting 0 and i know its wrong
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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)

by Level 11 User (81.5k points)

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