Find the indefinite integral of the function given by y=5x*e^2x?

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

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

We'll put u = 5x.
(1)

We'll differentiate both
sides:

du =5 dx (2)

We'll put
dv = e^2x (3)

We'll integrate both
sides:

Int dv = Int e^3x
dx

v = e^2x/2 (4)

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

Int udv =
5x*e^2x/2 - 5Int (e^2x/2)dx

Int  (5x*e^2x)dx
= 5x*e^2x/2 - 5*e^2x/4 + C