Question

Integral of xe^(x/3)

Answer 1

have you tried using integration by parts?

Answer 2

Wouldn't u substitution work?

Answer 3

did you try it? and succeed?

Answer 4

U= x
dV= e^(x/3)
etc.
try that and see if it works.

Answer 5

Use integration by parts three times.
∫ x e^(x/3) dx
let u = x : du = dx
dv = e^(x/3) : v = 3e^(x/3)
∫ x e^(x/3) dx = 3x e^(x/3) - ∫ 3e^(x/3) dx
= 3x e^(x/3) - 3 ∫e^(x/3) dx
= 3x e^(x/3) - 9e^(x/3) + C