Substitution method for integrating t / (t + 1)

[cmnalo]

Finding the indefinite integral

∫ t / (t + 1) dt

u = t + 1
du = dt

∫ t / u dt

I'm trying to set this problem up and don't think I'm doing it correctly? Any help would be great.

Answer: t-ln │t+1│ + c

 

[galactus]

You're on the right track.

Let \(\displaystyle \L\\u=t+1\) and \(\displaystyle \L\\du=dt\) and \(\displaystyle \L\\u-1=t\)

Then you have:

\(\displaystyle \L\\\int\frac{u-1}{u}du=\int{(1-\frac{1}{u})}du\)

 

[cmnalo]

I see where the -ln │u│ + c or -ln│t+1│+c comes from but I confused as to where the first (t) in the answer comes from?

 

[galactus]

cmnalo, you're being a silly goose. Integrate 1.

 

[cmnalo]

thanks