Standard Substitutions:
- For terms of form x2 + a2 or
, put x = a tanθ or a cotθ
For terms of form x2 - a2 or
, put x = a secθ or a cosecθ
(A) For terms of form a2 - x2 or
, put x = a sinθ or a cosθ
- If both
are present, then put x = a cosθ.
- For the type
.
- For type
, put the expression within the
bracket = t.
- For type
(n ∈ N, n> 1), put x+b/x+a= t.
- For
, n1,n2 ∈ N (and > 1), again put (x + a) = t (x + b)
Example: Evaluate
.
Solution:
![578_Standard Substitutions9.png](https://www.expertsmind.com/../CMSImages/578_Standard Substitutions9.png)
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