Integrate (2x)(e^x)dx

Solve via Integration by parts:

let u=2x and dv/dx=e^x

the function that is u and the one that is dv/dx is given by LATHE (easier to explain on whiteboard)

make the table: u=2x    =>    du/dx=2; dv/dx = e^x   =>   v=e^x

then use the formula integral of u(dv/dx)dx = uv - integral of v(du/dx)dx  =  (2x)(e^x) - (integral sign)(2e^x)dx  =  (2x)(e^x) - 2e^x + C [Dont Forget C]