<p>The following table lists the rules for differentiation and integration of inverse trigonometric functions.</p>
<p>Let \(\mathrm{f}\) be a function and \(a\) a constant, and \(C\) denotes an arbitrary constant.</p>
<div class="content-block content-block--table"><div class="table-container"><table><caption>Table of Inverse Trigonometric Formulas</caption><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Differentiation</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Integration</th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\[\frac{\mathrm{d}}{\mathrm{d}x} \arcsin \frac{x}{a} =  \frac{1}{\sqrt{a^2 - x^2}}\]</p></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\[\displaystyle\int \frac{1}{\sqrt{a^2 - x^2}} \, \mathrm{d}x = \arcsin \frac{x}{a} + C\]</td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\[\frac{\mathrm{d}}{\mathrm{d}x} \arctan \frac{x}{a} = \frac{a}{a^2 + x^2}\]</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\[\displaystyle\int \frac{1}{a^2 + x^2} \, \mathrm{d}x = \frac{1}{a} \arctan \frac{x}{a} + C\]</td></tr></tbody></table></div></div>

The following table lists the rules for differentiation and integration of inverse trigonometric functions.

Let \(\mathrm{f}\) be a function and \(a\) a constant, and \(C\) denotes an arbitrary constant.

Standard forms

Standard forms

Differentiation	Integration
\[\frac{\mathrm{d}}{\mathrm{d}x} \arcsin \frac{x}{a} = \frac{1}{\sqrt{a^2 - x^2}}\]	\[\displaystyle \displaystyle\int \frac{1}{\sqrt{a^2 - x^2}} \, \mathrm{d}x = \arcsin \frac{x}{a} + C\]
\[\frac{\mathrm{d}}{\mathrm{d}x} \arctan \frac{x}{a} = \frac{a}{a^2 + x^2}\]	\[\displaystyle \displaystyle\int \frac{1}{a^2 + x^2} \, \mathrm{d}x = \frac{1}{a} \arctan \frac{x}{a} + C\]