# Math Help - integral??

1. ## integral??

hey uhh.. my teacher never taught me how to differentiate log/ln functions or integrate them.. so i am asking, what is the integral of $ln(t^2 - 3t + 3)$

2. $\int ln(t^{2}-3t+3)dt$

This is a rather tough one if you've never been shown anything as you claim.

Try using parts.

Let $u=ln(t^{2}-3t+3), \;\ dv=dt, \;\ v=t, \;\ du=\frac{2t-3}{t^{2}-3t+3}dt$

3. Originally Posted by elpermic
hey uhh.. my teacher never taught me how to differentiate log/ln functions or integrate them.. so i am asking, what is the integral of $ln(t^2 - 3t + 3)$
I'd suggest to start by using integration by parts:

$\int u \, dv = uv - \int v \, du$.

Let $u = \ln (t^2 - 3t + 3) \Rightarrow du = \frac{2t - 3}{t^2 - 3t + 3} \, dt$ and $dv = dt \Rightarrow v = t$.

Now you have some spade work to do.

4. basically all you have to do is use the chain rule if you know that.

ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

hope that helps

5. Originally Posted by doneng
basically all you have to do is use the chain rule if you know that.

ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

hope that helps
What you mean is

Originally Posted by doneng
To get the derivative basically all you have to do is use the chain rule if you know that.

ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

hope that helps