The Indefinite Integral
SUGGESTED REFERENCE MATERIAL:
As you work through the problems listed below, you should reference Chapter 5.2 of the rec-
ommended textbook (or the equivalent chapter in your alternative textbook/online resource)
and your lecture notes.
EXPECTED SKILLS:
โขGiven a differentiation rule, be able to construct the associated indefinite integration
rule.
โขKnow how to integrate power functions (including polynomials), exponential functions,
& trigonometric functions.
PRACTICE PROBLEMS:
For problems 1 and 2, compute the indicated derivative and state a corresponding
integration formula.
1. d
dx ๎1
(2x+ 3)2๎
2. d
dx[xln xโx]
For problems 3-18, evaluate given indefinite integral and check your answer by
differentiation.
3. Z๎1
2x+x2๎dx
4. Z๎โx7+e๎dx
5. Z๎1
x3+ 3x3๎dx
6. Z๎3xโ2/3+xโ1/2+ 5x๎dx
7. Z๎4x4/3โ7โx๎dx
8. Z3 cos x dx
1
