Question

How do you integrate xe^(2x)dx? ...?

Answer 1

`\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)=(e^(2x))/(2), g'(x)=1 \\ \\ \rightarrow (1)/(2)xe^(2x)-(1)/(2)\int\limits e^(2x)dx \rightarrow (1)/(2)xe^(2x)-(1)/(4)e^(2x)+C`