Mathematics

This is integration by parts, where one function gets simpler when you differentiate it and the other stays manageable when you integrate it. Choose $u = 2x+1$ (which becomes the constant 2 when you differentiate) and $dv = e^{3x}\,dx$ (which stays exponential when integrated). The key is that the linear part vanishes after one application, leaving you with a straightforward exponential integral to finish.

This is integration by parts, where one function gets simpler when you differentiate it and the other stays manageable when you integrate it. Choose $u = 2x+1$ (which becomes the constant 2 when you differentiate) and $dv = e^{3x}\,dx$ (which stays exponential when integrated). The key is that the linear part vanishes after one application, leaving you with a straightforward exponential integral to finish.