12. Techniques of Integration

Which of the following integrals is improper?

In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

∫ from e to e^e of (ln(ln x) dx)

Which of the following integrals is improper because the interval of integration is infinite?

Evaluate the integral or state that it diverges. 

${\int }_{-\infty }^{-1}\frac{2}{x^3}dx$