Here are five separate problems. Show that the series 1/3^(ln(n)) converges and that the series 1/2^(ln(n)) diverges. integral (sqrt(x)*e^-sqrt(x)) dx integral (x/(sqrt(x-1)+2)) dx integral (1/(2+sin(x)+cos(x) integral (1-cos(x))^(5/2)) dx There are no other relevant equations. My attempts at solution lead nowhere and are too long-winded to post. I believe I am just missing one important premise I need to solve these. Any help would be appreciated.