Find the integral?

Question

Find the integral of (2 du)/(1+3u). Answer: (2/3)*ln abs(1+3u)+C abs means absolute value. Please show all your work. Thanks.

Answer 1

∫2/(1+3u)  du

 

let 1 + 3u = t

 

3du/dt = 1

du = dt/3

 

substitute

 

∫(2/3t)dt = 2/3∫1/t  dt = 2/3 ln t + C

 

substitute t = 1+3u

 

∫(2/3t)dt = 2/3 ln(1+3u)  + C

 

:)