You can break up the integral at any point or points you like. In this case, you could break it up into three integrals: pick a point c strictly between 0 and 1, and consider:
The original improper integral exists if and only if each of the three improper integrals exist.
2022-01-07Added 32 answers
Consider the change of variables . It transforms the interval into and removes one of the problem zeroes. It is easy to see from the resulting expression that the integral diverges.
2022-01-11Added 439 answers
Try to solve the integral. You'll find whether it converges. For example, with . Later on, you can study the limit . In this way, you ''kill two birds with a one shot''.
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