Question

l.le In Matlab try to determine the improper integral dz. Use the comparison test for im- proper integrals to show that this integral converges.

Answer 1

| # Integral Indefinite f-@(x) 1/(x+exp(x)); quad(f, 0,Inf) 3

Output ans0.80640

Note that

$\frac{1}{x+e^x}\le \frac{1}{e^x}=e^{-x}$ and

$\int_3^\infty e^{-x}dx<\infty$

So by comparison test, the given integral converges