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

integral. G' (x) = Vtan x and G(0) =4. 25. Evaluate the integral. cost (2 - sint)* dt 26. Evaluate the integral. 27. Use tabular integration to find the antiderivative. J (x2 - 3x) edx 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. ( x edx 30. Solve the initial value problem. dy = xe-2x and y =-1 when x = 0 dx 31. Solve the initial value problem. ay dx =(x+2) sin x and y = 2 when x = 0 32. Explain what is wrong with J Lf (x) g (x) +4h(x)-g(x)]dx =J f(x)g(x)dx+4f[h(x)-g(x) dx 33. Given J. f (x) dx =6 and J. f(x) dx =-3, find Sof (x) dx. 34. Use the Fundamental Theorem of Calculus to evaluate ) 1 x dx 35. Evaluate the integral: |cos - dx 4