# Homework Help: Trig Identity Integral

1. Oct 18, 2011

### theRukus

1. The problem statement, all variables and given/known data
I missed one class on trigonometric identities in integrals, and I feel that one is needed here:

$\int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dx$

2. Relevant equations

3. The attempt at a solution
Again, I'm unsure what to do. I think that it is a trig identity, but I could be wrong. I'll continue to try parts & substitutions..

Thanks!

2. Oct 18, 2011

### SammyS

Staff Emeritus
The derivative of acrtan(x) is 1/(x2+1), so the derivative of acrtan(x/3) is 3/(x2+9)

3. Oct 18, 2011

### Staff: Mentor

Split the integral into two integrals. The first can be done directly and the second can be done with an ordinary substitution. Integration by parts is not the way to go.

Do you know this differentiation formula?
$$\frac{d}{dx} tan^{-1}(x)?$$

4. Oct 18, 2011

### SammyS

Staff Emeritus
Notice that $\displaystyle \frac{d((f(x)^2)}{dx}=2f(x)f'(x)\,.$

That does that imply regarding $\displaystyle \int\ f(x)f\,'(x)\,dx\,?$