<p>A way to choose "\(u\)" is by applying the following LIATE rule:</p>
<p style="text-align: center">Increasing priority to be chosen as (u):</p>
<p>\[
\longleftarrow
\]</p>
<div class="content-block content-block--table"><div class="table-container"><table><caption>LIATE rule</caption><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;"><strong>L</strong></p></th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;"><strong>I</strong></p></th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;"><strong>A</strong></p></th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;"><strong>T</strong></p></th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;"><strong>E</strong></p></th></tr></thead><tbody><tr style="height: 38px;"><td style="height: 38px; min-height: 38px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;">Logarithmic, e.g., \(\ln x\), \(\mathrm{lg} x \)</p></td><td style="height: 38px; min-height: 38px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;">Inverse trigonometric, e.g., \(\arcsin, \arctan \)</p></td><td style="height: 38px; min-height: 38px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;">Algebraic, e.g., \(x^2, \sqrt{x}\)</p></td><td style="height: 38px; min-height: 38px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;">Trigonometric, e.g., \(\sin x, \cos x \)</p></td><td style="height: 38px; min-height: 38px; text-align: left; --cell-justify: flex-start"><p style="text-align: center;">Exponential, e.g., \(e^x\)</p></td></tr></tbody></table></div></div>

A way to choose "\(u\)" is by applying the following LIATE rule:

Integration by Parts

Techniques of  Integration

International Baccalaureate Higher Level Mathematics