Trig sub completing the square: complete square before substitution. Integrate 1/sqrt(x^2+4x-12).

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When we see a square root in the integral with a variable thing squared inside, we immediately think to try a trigonometric substitution!

Complete the square trigonometric substitution integral: complete square before substitution to fit the form of a pythagorean identity.

In this trig sub completing the square problem, we integrate 1/sqrt(x^2+4x-12). We complete the square before substitution in the denominator, then we apply a pythagorean trig identity to make a trigonometric substitution. To clean up the answer, we have to compute the tangent of an inverse secant, which we do using a geometric construction. Finally, we discuss the appearance of the final answer for the integral of 1/sqrt(x^2+4x-12), which can change depending on what constants are absorbed into the arbitrary constant, C.

[darcash]

What is the point of Euler’s substitution? Is it ever faster than trig sub? I learned how to do it recently but I’m finding they’re interchangeable so far..😅

[Brekstahkid]

Dislike because you're doing an easy example.