I need answer all questions

Question 1 Use techniques of integration to evaluate the following integrals. (a) Evaluate S xe* dx. (6 marks) (b) Determine the exact value of , 2 -dx. 1 x2 +3x+2 Express your answer in the form of In ( ), where C, D are constants to be determined. (7 marks) (c) Determine the exact value of f, x In(x2) dx. (7 marks) Question 2 (a) d sinx Solve JT "t2 dt using Fundamental Theorem of Calculus, simplifying your answer as much as possible. (6 marks) ( b ) In x Determine the derivative of f (x) = 2. Hence, determine the exact value of the integral re 2-2In x -dx. x3 (14 marks)