Title: Trigonometric Substitutions

Use trigonometric substitution to evaluate integrals involving the radicals,

Case I:

Example 1:

Solution:

Then,

Example 2:

Solution:

Let x = 2 sin θ, dx = 2 cosθ dθ

Case II:

Example 3:

Solution:

Then,

Case III:

Example 4:

Solution:

Then,

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