Solve 28, 30, 31. Show every step of work. And explain every step in depth.

25. Evaluate the integral. cost dt 26. Evaluate the integral. (2- sint)* 27. Use tabular integration to find the antiderivative. I ( x2 - 3x) edx sm 28. Use separation of variables to solve the initial value problem. y' = (xy ) and y =1 when x =1 29. Evaluate the integral using a substitution prior to integration by parts. ( x2edx 30. Solve the initial value problem. dy - e-2x and y =-1 when x = 0 dx 31. Solve the initial value problem. dy = (x+ 2) sin x and y = 2 when x = 0 dx 32. Explain what is wrong with J Lf (x)g (x) +4h(x) -g(x)]dx =f f(x)g(x)dx +4f[h(x)-g(x) dx 33. Given J. f (x) dx = 6 and ]. f (x) dx =-3, find S, f (x) dx. 34. Use the Fundamental Theorem of Calculus to evaluate ) , 73 dx 35. Evaluate the integral: Scos - dx