1. Complete the following basic antiderivative problems. (a) Evaluate the given indefinite integral (don't forget the "+C"): (i) 3x^3+ 7x + 5 dx =

(ii) sin(3x) + sec2(x) dx =

(iii) 1 /x + 1 / x^2 dx =

(iv) 3x2sin(x) + x3cos(x) dx =

(v) cos(x) + x sin(x) / (cos2(x)) dx =

(b) For each of the following parts, find f (x) described by the initial value problem. (i) f (x) = sin(x) and f (0) = 2.

(ii) f(x) = 4x^2, f (0) = 3, and f (0) = 4