Is there a possible error in the integration on the solution to problem 1? The order of the variables changes from equation 2 to equation 3. The integration is a partial fraction decomposition but shouldn’t there be a minus sign in term one of equation 4?
It appears that the evaluated integral for problem 1 does match the solution given for problem 1. Use absolute value signs for the first integral until the integral is evaluated at L and -L. For the second integral use "u" substitution carefully and observe the proper sign that arise in the substitution.