Learn trigonometric substitution techniques for solving complex integrals in this comprehensive calculus video. Master integration methods for various forms including sqrt(x^2+1), sqrt(x^2-1), and sqrt(1-x^2). Explore substitutions like x=a*sinθ, x=a*secθ, and x=a*tanθ to simplify challenging integrals. Practice with numerous examples, including integrals involving 1/sqrt(x^2+16), sqrt(1-4x^2), and sqrt(x^2-9)/x^3. Gain proficiency in handling integrals with mixed terms like sqrt(x^2+2x) and x*sqrt(1-x^4). Compare integration techniques for similar expressions such as sqrt(1+x^2)/x versus x/sqrt(1+x^2). Ideal for calculus students seeking to enhance their integration skills and problem-solving abilities in trigonometric substitution.