# Let's do some calculus! (50)

Calculus Level 5

$\large \int_0^1 \left\{(-1)^{\left\lfloor 1/x \right\rfloor}\cdot \frac 1x \right\} \ \mathrm{d}x$

If the value of the above integral can be represented as $$a + \ln \left( \dfrac b\pi \right)$$ for positive integers $$a$$ and $$b$$, find $$a+b$$.

Notations: