Methods of Integration: Integration by Substitution



  • ∫ tan x dx = log | sec x |  + C
  • ∫ cot x dx = log | sin x | + C
  • ∫ sec x dx = log | sec x + tan x | + C
  • ∫ cosec x dx = log | cosec x – cot x | + C


The given integral ∫f(x)dx  can be transformed into another form by changing 
the independent variable x to t by substituting x = g (t).
Consider             I =∫ f x dx   
Put x = g(t) so that `(dx)/(dt)` = g'(t)
dx = g′(t) dt
Thus   I =∫f(x) dx ∫f ( g (t))g'( t) dt 
This change of variable formula is one of the important tools available to us in the name of integration by substitution.

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Indefinite Integration by U Substitution [00:29:56]

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