Determine whether the improper integral converges or diverge

Determine whether the improper integral converges or diverges. If the integral converges, evaluate its value.

a)

b)

Solution

a)
=x^-0.9+1/(-0.9+1)=x^0.1/(0.1) |0..1=1

so it converges to 1

b)

=ln(x²+1)|1..=-ln(2)=

so it diverges

the integral can be done directly (the derivative of ln(x²+1) is 2x/(x²+1))