For each of the improper integrals below, if the comparison test applies, enter either A or B followed by one letter from C to K that best applies, and if the comparison test does not apply, enter only L. For example, one possible answer is BF, and another one is L.

Hint: $0 < e^{-x}\leq 1$ for $x\geq 1$.

1. $\displaystyle \int_1^\infty \frac{x}{\sqrt{x^6+3}}\,dx$
2. $\displaystyle \int_1^\infty \frac{8+\sin(x)}{\sqrt{x-0.3}}\,dx$
3. $\displaystyle \int_1^\infty \frac{e^{-x}}{x^2}\,dx$
4. $\displaystyle \int_1^\infty \frac{\cos^2(x)}{x^2+3}\,dx$
5. $\displaystyle \int_1^\infty \frac{1}{x^2+3}\,dx$

A. The integral is convergent
B. The integral is divergent
C. by comparison to $\displaystyle\int_1^\infty\frac{1}{x^2-3}\,dx$.
D. by comparison to $\displaystyle\int_1^\infty\frac{1}{x^2+3}\,dx$.
E. by comparison to $\displaystyle\int_1^\infty\frac{\cos^2(x)}{x^2}\,dx$.
F. by comparison to $\displaystyle\int_1^\infty\frac{e^x}{x^2}\,dx$.
G. by comparison to $\displaystyle\int_1^\infty\frac{-e^{-x}}{2x}\,dx$.
H. by comparison to $\displaystyle\int_1^\infty\frac{1}{\sqrt{x}}\,dx$.
I. by comparison to $\displaystyle\int_1^\infty\frac{1}{\sqrt{x^5}}\,dx$.
J. by comparison to $\displaystyle\int_1^\infty\frac{1}{x^2}\,dx$.
K. by comparison to $\displaystyle\int_1^\infty\frac{1}{x^3}\,dx$.
L. The comparison test does not apply.

You can earn partial credit on this problem.