# Trigonometric Substitution | Techniques of Integration

Trigonometric substitution is employed to integrate expressions involving functions of (*a*^{2} − *u*^{2}), (*a*^{2} + *u*^{2}), and (*u*^{2} − *a*^{2}) where "*a*" is a constant and "*u*" is any algebraic function. Substitutions convert the respective functions to expressions in terms of trigonometric functions. The substitution is more useful but not limited to functions involving radicals.

**Use the following suggestions:**

When the integrand involves...

- (
*a*^{2}−*u*^{2}), try*u*=*a*sin θ - (
*a*^{2}+*u*^{2}), try*u*=*a*tan θ - (
*u*^{2}−*a*^{2}), try*u*=*a*sec θ

The substitution may be represented geometrically by constructing a right triangle.

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