# Thread: Need some help starting a def integral!

1. ## Need some help starting a def integral!

I need to integrate $\int arctan(1/x)$ dx from 1 to $\sqrt{3}$. If someone could please show me the first few steps, like the substitutions, that would be great!
Thanks

2. ## Re: Need some help starting a def integral!

Have you tried with integration by parts?
$\int_{1}^{\sqrt{3}} \arctan\left(\frac{1}{x}\right)dx=\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}-\int_{1}^{\sqrt{3}} d\left[\arctan\left(\frac{1}{x}\right)\right]\cdot x$
$=\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}+\int_{1}^{\sqrt{3}} \frac{x}{x^2+1}dx$

For the last integral you just have to use a simple substitution.

3. ## Re: Need some help starting a def integral!

Oh, okay! So u=arctan(1/x) and dv=dx. It all makes sense now, thanks!

4. ## Re: Need some help starting a def integral!

Originally Posted by NeedDirection
Oh, okay! So u=arctan(1/x) and dv=dx. It all makes sense now, thanks!
Indeed! I think you can figure out the last integral .