Improper integral convergence or divergence.

[crazy_nuttie]

Homework Statement

Use Comparison Theorem to determine whether the integral is convergent or divergent:

integral from 0 to infinity of: arctan(x) / (2 + e^x)

Should look like this: http://bit.ly/cAhytV

Homework Equations

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The Attempt at a Solution

I tried to compare this with the integral from 0 to infinity of 1/e^x, but that didnt succeed since 1/e^x converges and the given function is less than 1/e^x. I am not sure what to compare this with

 

[LCKurtz]

Homework Statement

Use Comparison Theorem to determine whether the integral is convergent or divergent:

integral from 0 to infinity of: arctan(x) / (2 + e^x)

Should look like this: http://bit.ly/cAhytV

Homework Equations

--

The Attempt at a Solution

I tried to compare this with the integral from 0 to infinity of 1/e^x, but that didnt succeed since 1/e^x converges and the given function is less than 1/e^x. I am not sure what to compare this with

Not sure why you chose 1/e^x since \arctan x \le \pi/2 but not bounded by 1.

Anyway, why wouldn't you have succeeded if your integral is less than a known convergent integral? Your problem would be if your unknown integral was greater than a known convergent integral.