Integral of (x² - 1)^-1.5 with trigonometric substitution

In this video, I will show you how to use trigonometric substitution to solve the integral of (x² - 1)^-1.5. You should use trigonometric subsitution when you cannot solve the integral with u substitution or integration by parts. There are three forms you need to know: the square root of (x^2-a^2), the square root of (x^2+a^2), and the square root of (a^2-x^2). In the first case, x=asinθ. In the second case, x = atanθ. In the third case, x = asecθ. Trigonometry substitution is an important topic that calculus students will learn either in high school or in university.

[@calculus988]

Nice video

[@QuocDatPhung]

Thank you Calculus! The full video for trig substitution will be out in a few weeks. This is just a small part of it. The next problem will be the integral of sqrt(3-7x^2)