Integral of a Shifted Sum of Squares

Rarely Tested

Integral of a Shifted Sum of Squares

For $$a>0$$:

$$\int\frac{dx}{(x-h)^2+a^2}=\frac{1}{a}\tan^{-1}\left(\frac{x-h}{a}\right)+C$$

Usage

- Used after completing the square when the quadratic denominator is positive.

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