There are four integrals:

Question

1) definite integral x/(1+x^4)dx b/w 0_infinity

2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity

3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity

4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity

Which of these integrals converge. First of all, what does it mean "converge"? How do you compare to "pure" powers of x?

How would you compute the exact value of at least one of the convergent integrals?

thanks