I need help with this problems

Problem 1. Evaluate the following integral: (1) 1 (2+1) -dx, 1 In Edx. (2) Jo Vi Problem 2 . Determine if the following series converge (absolutely or conditionally ) or diverge. You must make a determination and then justify it for each series: (1) 2 In(2n241)) (2) > 2+1 3 1 (if it converges, find its actual value), n=1 n= 1 (3 ) (n)!(n+ 1 ) ! n cos (n) ( - 1 ) n+1 (n + 6 ) (2n)! ( 4 ) 3n ( 5 ) E n.=1 n= n=1 nvn+2 Problem 3. Find the interval of convergence for the following series. Must show your work. (1) E n1+4 ( 2 ) 572-T (2 - 2)", (3 ) E 2" (3x - 2)". n=0 1=1 Problem 4. Approximate the value of the series so that the error is within 0.001: (1 ) E (-1 )n+1 00 Vn (2) E(-1)n+] In(1 + 2). n=1 n=1