1. Find the following indefinite integrals:
| a. | ∫ 15x4 dx | b. | ∫ (4x3 + 6x) dx | c. | ∫ (7x6 − 6x5 − 5x4) dx |
| d. | ∫ (5x3 − 4x2 + x − 7) dx | e. | ∫ (3x − 1)(2x + 6) dx | f. | ∫ (2x +1)2 dx |
| g. | ∫ -2(x2 + 3) dx | h. | ∫ 3x2(2x2 − 4) dx | i. | ∫ x2(2x2 − 4)2 dx |
| j. | ∫  dx |
k. | ∫  dx |
l. |  |
2.Anti-differentiate the following derived functions:
a. f '(x) = 5x2 − 8x + 2
b. g'(x) = 2x(x − 3)
c. dy/dx = (x − 2)(x + 3)
3. Integrate to find the original function for each of the following derived functions:
| Derived function | Conditions | |
| a. | f '(x) = 6x2 | f(2) = 12 |
| b. | g '(x) = 2x + 3 | g(1) = 4 |
| c. | h '(x) = 3x2 + x − 10 | f(3) = -5 |
| d. | dy/dx = 3(x − 2)2 | y = 1 when x = 2 |
