# 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 .

Then ,

and ,

It is also quite obvious that we can the following picture is defined from our substitution:

So,

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