Question

How do you show whether the improper integral `int dx / (x^2 + sinx)` converges or diverges from 2 to infinity?

Answer 1

`int_2^oo dx / (x^2 + sinx) lelog_e(sqrt(3))`

Explanation:

`int dx / (x^2 + sinx)le int dx/(x^2-1)`

so

`int_2^oo dx / (x^2 + sinx) lelim_{x->oo}log_e sqrt(abs(1-x)/abs(1+x)) +log_e(sqrt(3))`

so

`int_2^oo dx / (x^2 + sinx) lelog_e(sqrt(3))`