basic antiderivative rules

"Basic" antiderivatives are ones that we should be able to do "in our head" because of our knowledge of derivatives. Recall that among the basic derivative rules we know are the following.
Derivatives of Basic Functions:
  ( e x )' = e x
  ( a x )' = ln(a) a x
  ( sin(x) )' = cos(x)
  ( cos(x) )' = -sin(x)
  ( ln(x) )' = 1 / x
 
  (xn) ' = n xn - 1
  ( tan(x) )' = 1 / ( cos(x) )2
  ( arctan(x) )' = 1 / ( 1 + x2 )
  ( arcsin(x) )' = 1 / sqrt( 1 - x2 )
  ( arccos(x) )' = -1 / sqrt( 1 - x2 )
So, if someone asks for the antiderivative of anything like x5/ 3, sin(x), or (22/5)x, we should be able to write down the antiderivative immediately:
ò x5/ 3 dx = (1 / (8/3)) x8/ 3 + C
= (3/8) x8/ 3 + C
ò sin(x) dx = -1*cos(x) + C
   
ò (22/5)x dx = (1 / ln(22/5)) (22/5)x + C
    
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Tutorial links:
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see a basic antidifferentiation example
do a practice test on basic antidifferentiation
see a random integration example
do a practice gateway
int tutorial: elementary antidiff
Last Modified: Fri Aug 31 14:48:59 EDT 2001
Comments to glarose@umich.edu
©2001 Gavin LaRose, UM Math Dept.