Integral Test for Convergence Practice Test

Converges because $\int_1^{\infty} \frac{1}{(x^2+1)^{3/4}},dx$ converges.

Diverges because $\int_1^{\infty} \frac{1}{x^{3/2}},dx$ diverges.

Diverges because $\int_1^{\infty} \frac{1}{(x^2+1)^{3/4}},dx$ converges.

Converges because $\int_1^{\infty} \frac{1}{\sqrt{x^2+1}},dx$ converges.

Diverges because $\int_1^{\infty} (x^2+1)^{3/4},dx$ diverges.