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The integral is .
Rewrite the integral as
Consider the second integral on right side .
Now apply comparison value theorem for above integral.
Consider the fact and it implies that .
Comparison theorem:
Suppose that and are continuous functions with for ,
1. If is convergent, then is convergent.
2.If is divergent, then is also divergent.
Here and
Since is a finite value, it is convergent.
By comparison theorem, is convergent.
is convergent, it follows that is also convergent.
and are convergent, then is convergent.
is convergent.
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