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Proof that an Integral Is Divergent

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f(x) = arctan(x)/ x for x !=0
f(x) = 1 for = 0

f'(x) = 1/(x+x^3) -arctan(x)/x^2 for x !=0
f'(x) = 0 for x = 0

F is the integral from 0 to x of f(x)
Know that F(x) is strictly increasing and F(x) = F(-x)

Show that lim F(x) = infinity
when x goes to infinity

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Solution Summary

We prove that a particular integral is divergent.

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