Question

Find the integral of (2 du)/(1+3u). (Answer: (2/3)*ln abs(1+3u)+C where abs is absolute value.)

Answer 1

\[\int\frac{2}{1+3u}~du\]
Substitute \(t=1+3u\), then \(dt=3~du\), or \(\dfrac{1}{3}dt=du\):
\[\frac{2}{3}\int\frac{dt}{t}\]

Answer 2

And then?

Answer 3

I get it now, thanks.

Answer 4

You're welcome, sorry about the delay.