помогите, Интеграл от x*e^3x чему равен?

Интеграл: S (x * e^3x * dx)

Интегрируем по частям.

= 1/3 * x * e^3x - S (1/3 * e^3x * dx) = 1/3 * x * e^3x - 1/9 * e^3x = 1/9 * e^3x * (3x - 1

We'll integrate by parts. For this reason, we'll consider the formula:

Int udv = u*v - Int vdu (*)

We'll put u = x. (1)

We'll differentiate both sides:

du = dx (2)

We'll put dv = e^3x (3)

We'll integrate both sides:

Int dv = Int e^3x dx

v = e^3x/3 (4)

We'll substitute (1) , (2) , (3) and (4) in (*):

Int udv = x*e^3x/3 - Int (e^3x/3)dx

Int (x*e^3x)dx = x*e^3x/3 - e^3x/9 + C