<p>Notes</p>
<ol class="num-list"><li><div class="list-item-paragraph">Integrating a single function: If a single function \(\mathrm{f}(x)\) cannot be integrated directly, take<br>\[u = \mathrm{f}(x) \text{ and } \frac{\mathrm{d}v}{\mathrm{d}x} = 1.\]</div></li><li><div class="list-item-content"><span class="list-item-text">LIATE rule provides one of the ways to solve the integration, but it may not be the only way</span></div></li><li><div class="list-item-paragraph">LIATE rule works for most of the integrations in the IB exam, but there are some counterexamples. For example, <br>\( \displaystyle \displaystyle\int x^3 \sin x^2 \, \mathrm{d}x\) (\(u = x^2\)) and \(\displaystyle \displaystyle\int \sin^n x \, \mathrm{d}x\) (\(u = \sin^{n-1} x\)) </div></li></ol>

Integrating a Single Function: If a single function \(\mathrm{f}(x)\) cannot be integrated directly, take\n\[u = \mathrm{f}(x) \text{ and } \frac{\mathrm{d}v}{\mathrm{d}x} = 1\]

Integrating a single function: If a single function \(\mathrm{f}(x)\) cannot be integrated directly, take
\[u = \mathrm{f}(x) \text{ and } \frac{\mathrm{d}v}{\mathrm{d}x} = 1.\]

LIATE rule provides one of the ways to solve the integration, but it may not be the only way

LIATE rule works for most of the integrations in the IB exam, but there are some counterexamples. For example, \(\displaystyle \displaystyle\int x^3 \sin x^2 \, \mathrm{d}x\) (\(u = x^2\)) and \(\displaystyle \displaystyle\int \sin^n x \, \mathrm{d}x\) (\(u = \sin^{n-1} x\))

LIATE rule works for most of the integrations in the IB exam, but there are some counterexamples. For example, 
\( \displaystyle \displaystyle \displaystyle\int x^3 \sin x^2 \, \mathrm{d}x\) (\(u = x^2\)) and \(\displaystyle \displaystyle \displaystyle\int \sin^n x \, \mathrm{d}x\) (\(u = \sin^{n-1} x\)) 

Notes on applying LIATE rule

Notes on applying LIATE rule