Lesson

INTEGRATIONS RESULTING IN INVERSE TRIGONOMETRIC FUNCTIONS

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$$ \begin{align} \displaystyle \int \frac{1}{\sqrt{1-x^2}} dx &= \sin^{-1} x + C \\ \int \frac{1}{\sqrt{a^2-x^2}} dx &= \sin^{-1} \frac{x}{a} + C \end{align} $$

$$ \begin{align} \displaystyle \int \frac{-1}{\sqrt{1-x^2}} dx &= \cos^{-1} x + C \\ \int \frac{-1}{\sqrt{a^2-x^2}} dx &= \cos^{-1} \frac{x}{a} + C \end{align} $$

$$ \begin{align} \displaystyle \int \frac{1}{1+x^2} dx &= \tan^{-1} x + C \\ \int \frac{1}{a^2 + x^2} dx &= \frac{1}{a} \tan^{-1} \frac{x}{a} + C \end{align} $$