This material is based upon work supported by the
National Science Foundation
under Grant No. DUE-0336493


STEP- Science, Technology, Engineering, and Mathematics Talent Expansion Program
  NOTE:

 

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Integration Formulas
 

Remember that u'dx = du and may be replaced by du.

bullet bullet dx = x + c
bullet bullet k f(x) dx = k f(x) dx
bullet bullet [f(x) ± g(x)]dx = f(x)dx ± g(x)dx
GENERAL SPECIFIC

un u' dx = ((un + 1)/(n + 1)) + c
(u'/u)dx = ln|u| + c
eu u' dx = eu + c
cosu * u'dx = sinu + c
sinu * u'dx = -cosu + c
sec2u * u'dx = tanu + c
tanu * u'dx = -ln |cosu| + c or ln |secu| + c
cotu * u'dx = ln |sinu| + c
au * u'dx = ((au)/(lna)) + c
secu * tanu * u'dx = secu + c
csc2u * u'dx = -cotu + c
cscu cot u * u' dx = -cscu + c
(u'/(a2 + u2))dx = (1/a)arctan(u/a) + c
(u'/(SQRT(a2 - u2)))dx = arcsin(u/a) + c
auu' dx = ((au)/(ln a)) + c
 
xn dx = ((xn + 1)/(n + 1)) + c
(1/x)dx OR (dx/x) = ln|x| + c
exdx = ex + c
cosx dx = sin x + c
sinx dx = -cos x + c
sec2x dx = tan x + c
tanx dx = -ln |cosx| + c or ln |secx| + c
cotx dx = ln |sinx| + c
ax dx = ((ax)/(ln a)) + c
secx tanx dx = sec x + c
csc2x dx - -cotx + c
cscx cotx dx = -csc x
dx/(a2 + x2) dx = 1/a arctan (x/a) + c
dx/(SQRT(a2 - x2))dx = arcsin (x/a) + c
ax dx = ((ax)/(ln a)) + c
 
 

                                  

 

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the
National Science Foundation.