Calculate the indefinite integral of x*e^3x.

giorgiana1976 | Student

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

neela | Student

To find Int x*e^x dx.

We know that Int  (uv) = u*Int vdx - Int (u'*int vdx) dx.

Therefore Int xe^x dx = x*Int e^xdx - Int {x'*int e^xdx}dx

Int xe^xdx = xe^x - Int{1*e^x}dx.

Int xe^xdx = xe^x - e^x +C, where C is a constant.

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