Question

Integral Question, is it convergent or divergent?

Answer 1

\[\int\limits_{1}^{\infty} 38 [(2+e ^{-x})/x]\]

Answer 2

It looks bigger than 2/x to me, and since 1/x integral diverges, this one does too.

Answer 3

its divergent.... thx...

Answer 4

If we rewrite,
\[ \int_1^\infty \frac{38(2+e^{-x})}{x} dx = 38\left(\int_1^\infty \frac{2}{x} dx + \int_1^\infty \frac{e^{-x}}{x} \right)
\]
We see that the first integral on the right hand side diverges and the second converges. Hence their sum diverges as well.