table of integrals
Post on 11-Dec-2015
218 Views
Preview:
DESCRIPTION
A table of integrals for easy reference
TRANSCRIPT
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.
top related