∫∞01x2−1
It was said that this integral is divergent. I have tried splitting the integral. ∫101x2−1+∫∞11x2−1
Using this, I tried to prove ∫101x2−1 is divergent by comparison test, but there are no functions that lie under 1x2−1 that diverge (at least that I can think of).
I know the function diverges by Wolfram Alpha, but am struggling to prove it.
Answer
Notice that
1x2−1=1x+1⋅1x−1≥131x−1
for 1≤x≤2. Now compute
∫2tdxx−1.
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