Integrals | Trigonometric Substitution (Example 2)

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Some useful identities:

√(a^2−x^2 ) 1−sin^2⁡θ=cos^2⁡θ x=asin⁡θ
√(a^2+x^2 ) 1+tan^2⁡θ=sec^2⁡θ x=atan⁡θ
√(x^2−a^2 ) sec^2⁡θ−1=tan^2⁡θ x=asec⁡θ

This requires inverse substitution.

Step 1: Set your x and find the derivative.
Step 2: Substitute your x and dx back into the original equation
Step 3: Use the appropriate trigonometric identity
Step 4: Simplify
Step 5: Integrate
Step 6: Convert back to original in terms of x