Indefinite Integrals


   
 
Integration by Substitution
Integration of the form
 
 
 
 
Put g(x) = t
 
Differentiating g(x) with respect to t, we have
 
g'(x) dx = dt
 
 
F(t) + C
 
F(g(x)) + C
 
Note 1:
 
 
Note 2:
 
 
Example:
 
 
Suggested answer:
 
 
 
 
 
 
Put tanx = t such that sec2xdx = dt
 
 
 
 
Integration using trigonometric identities
When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference.
 
(1)
 
(2)
 
(3)
 
(4)
 
(5)
 
 
(7)
 
(8)
 
Example:
 
Integrate the function sinx. sin2x sin3x.
 
Suggested answer:
 
 
 
 
 
 
 
 
 
 
     
   
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