Problem 1. (1) The integral 1 So + √√x(1+x)dx is improper in both ways we have discussed in class: the domain is unbounded (there is an ∞ as a bound) and one of the bounds is an asymptote. One way to calculate this integral is to write it as 1 1 1 r∞ 1 -dx = + √√√x(1+x) √√x(1+x) √√x(1+x) x) Our original integral converges if both integrals on the right hand side of the above equation converge. Use u-substitution to evaluate these integrals and calculate the value of the original integral.

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