Solving an integral of form $ F(x)=\int (2x-1)e^{2x}\ dx $

Question

I have this integral in a worksheet please help me solve it

$$ F(x)=\int (2x-1)e^{2x}\ dx $$

Answer 1

Let $u = (2x - 1)$ and $dv = e^{2x}dx$. Now continue with integration by parts.

Answer 2

You have a product... if you differentiate the first term of the product and integrate the second, the integral simplifies.