Integration by trigonometric substitution
integration by trigonometric substitution:
One of the most powerful techniques of integration is Integration by trigonometric substitution.
Integration by trigonometric substitution is similar technique to integration by substitution .
In integration by trigonometric substitution we substitute a variable by another trigonometrical variable.
We can integrate the integrals which involves , or .
It is obvious that substitution turns into ; the substitution turns into into and the substitution turns into .
These substitutions makes then resulting function easily integrable.
Examples of integration by trigonometric substitution:
Let us try to integrate the function:
Let us substitute .
It is also quite obvious that we can the following picture is defined from our substitution:
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