Summary of Trig Substitution Here is a table of diﬀerent trig substitutions and how they can be useful. If your integrand contains Make substitution To get √ a 2 − x2 x = a cos θ or x = a sin θ a sin θ or a cos θ √ a2 + x2 x = a tan θ a sec θ √ x2 − a2 x = a sec θ a tan θ These are the three basic forms which are integrated using trig substitution. In general, you use trig substitution to replace the square root of a quadratic function by a trigonometric function. Once you’ve done this, integrate, then use what we’ve learned about right triangles and undoing trig substitution to get a ﬁnal answer.

Summary of Trig Substitution

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