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Learn how to solve integrals using trigonometric substitution in Calculus. This lesson explains when to use trig sub, how to choose the correct substitution, and how to apply identities to simplify and evaluate integrals. Every step is shown clearly so you can follow along and understand the process from substitution to back-substitution. Topics in this video include: How to recognize when trig substitution is needed Substitutions for x^2 plus a^2, a^2 minus x^2, and x^2 minus a^2 Using Pythagorean identities with trig sub Integrals with square roots and quadratic expressions Example with integral of 1 over x^2 times square root of 16 minus x^2 Example with integral of square root of 9x^2 minus 63 over x Example with integral of x^2 over (4x^2 plus 1)^2 Example with integral of x^2 over square root of 4 plus x^6 Definite integral with (1 minus x^2)^(3/2) over x^6 Example with integral of dx over x times square root of 25x^2 plus 4 Connections to inverse trig functions like arc sine, arc tangent, and secant inverse Why some integrals are better solved with u substitution instead of trig substitution This video is great for Calculus 2 students, AP Calculus AB and BC review, and anyone practicing integration strategies for college-level math. For more video lessons and additional resources, visit www.xomath.com.