A Short Table of Integrals In all formulas, u is a function and a is a constant. You may need to use substitutions to make your integral match one of the formulas

1. un du! =un+1

n +1+ c,!n " #1

2. 1udu! = ln u + c

3. eu du! = eu + c

4. uneu du! = uneu " n un"1eu du! , where n is a positive integer

5. sinudu! = " cosu + c

6. cosudu! = sinu + c

7. 1

u2 + a2du! =

1atan"1 u

a+ c

8. 1

u2 ! a2du" =

12aln u ! au + a

+ c or 1

a2 ! u2du" =

12aln u + au ! a

+ c

9. 1a2 ! u2

du" = sin!1 ua+ c

10. a2 ! u2 du" =u2

a2 ! u2 + a2

2sin!1 u

a+ c

11. 1u2 ± a2

du! = ln u + u2 ± a2( ) + c

12. u2 ± a2 du! =u2

u2 ± a2 ± a2

2ln u + u2 ± a2( ) + c

Integration by parts: udv! = uv " vdu! where u and v are functions.