Question

how do you integrate xe^(2x)dx?

Answer 1

Did you try substitution?

Answer 2

use integrate by part.

Answer 3

how do you integrate by part?

Answer 4

udv=uv−(integral)vdu

Answer 5

integral before the udv

Answer 6

\[\int\limits f(x)g(x)dx= F(x)g(x)-\int\limits F(x)g'(x)dx\]
F(x)= the antiderivative of f(x) and g'(x)= the derivative of g(x)
\[\int\limits xe^{2x}dx \rightarrow f(x)=e^{2x}, g(x)=x, F(x)=\frac{e^{2x}}{2}, g'(x)=1\]
\[\rightarrow \frac{1}{2}xe^{2x}-\frac{1}{2}\int\limits e^{2x}dx \rightarrow \frac{1}{2}xe^{2x}-\frac{1}{4}e^{2x}+C\]