Another integration problem: int [(t^2 + 1) / (t + 1)] dt

[hank]

Here's my problem, and as far as I can get.

\(\displaystyle \L \int\, {\frac{t^2\, +\, 1}{t\, +\, 1}}\, dt\)

The way I read this, I should break the integral up into two parts.:

\(\displaystyle \L \int\, \left(\frac{t^2 }{t\, +\, 1}\, +\, \frac{1}{t\, +\, 1}\, \right)\, dt\)

I was then thinking that I would perform u substitution, and I was thinking of using t+1 for the sub. However, I don't know what to do with that t^2 then. Can someone fill in the steps for me?

I can't find an example of this problem in my book or notes.

 

[galactus]

Notice the power of the numerator is greater than the power of the denominator. When you see that, try dividing.

Dividing and you'll get:

\(\displaystyle \L\\\frac{t^{2}+1}{t+1}=\frac{2}{t+1}+t-1\)

Now, it's easier to integrate, ain't it?.