I need to integrate $\displaystyle \int arctan(1/x)$ dx from 1 to $\displaystyle \sqrt{3}$. If someone could please show me the first few steps, like the substitutions, that would be great!
Thanks
Have you tried with integration by parts?
$\displaystyle \int_{1}^{\sqrt{3}} \arctan\left(\frac{1}{x}\right)dx=\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}-\int_{1}^{\sqrt{3}} d\left[\arctan\left(\frac{1}{x}\right)\right]\cdot x$
$\displaystyle =\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}+\int_{1}^{\sqrt{3}} \frac{x}{x^2+1}dx$
For the last integral you just have to use a simple substitution.