Problem 5. (10 points) Suppose the following facts are given: . tan'(x) = sec2(x) = 1 + tan?(x) . If u = tan(?), then sin(x) = 2u 1+42, COs(x) = 1-u2 Use these facts to calculate the integral } - cos(x) roar dx and S 1 dx. (Hint: use u- sin (I) -2 cos(I) substitution.)