Integral and limit

Just two examples :

• Find the limit, when a approachs + $\infty$, of :
  $$\int_{2}^{a}$$$${\frac{{1}}{{x^2}}}$$ dx
  Input :
  limit(integrate(1/(x^2),x,2,a),a,+(infinity))
  Output (if a is not formal then input purge(a)) :
  1/2
• Find the limit, when a approachs + $\infty$, of :
  $$\int_{2}^{a}$$($${\frac{{x}}{{x^2-1}}}$$ + ln($${\frac{{x+1}}{{x-1}}}$$)) dx
  Input :
  limit(integrate(x/(x^2-1)+log((x+1)/(x-1)),x,2,a),
  a,+(infinity))
  Output (if a is not formal then input purge(a)) :
  +(infinity)