Problema 10

Fie $f:(1,\infty)\to\mathbb{R}$, $f(y)=\displaystyle\int_0^y \dfrac{1}{x^2-2x+y}\,dx$. Calculați $\displaystyle\int_2^{10} f(y)\,dy$.

a) $3\pi$; b) $2\pi$; c) $\dfrac{5\pi}{3}$; d) $\pi$; e) $\dfrac{\pi}{2}$; f) $\dfrac{3\pi}{2}$.