- #1
b0rsuk
- 5
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Homework Statement
[tex]\int x e^-3x dx[/tex]
Homework Equations
[tex]\int f(x)g'(x) = f(x)g(x) - \int f'(x) g(x)[/tex]
Integration by substitution not allowed
The Attempt at a Solution
[tex] f(x) = x, f'(x) = 1, g'(x) = e^{-3x}, g(x) = \int e^{-3x} dx = -\frac{1}{3}e^{-3x}[/tex]
[tex]\int x e^{-3x} dx = x(-\frac{1}{3})e^{-3x} - \int - \frac{1}{3} e^{-3x} dx = [/tex]
[tex]= -\frac{1}{3} x e^{-3x} + \frac{1}{3} \int e^{-3x} dx =-\frac{1}{3} x e^{-3x} -\frac{1}{9} e^{-3x} + C[/tex]
Which is incorrect. I'm not sure how to integrate e^(-3x) properly.