Notes on applying LIATE rule

Notes

1. Integrating a single function: If a single function \(\mathrm{f}(x)\) cannot be integrated directly, take
   \[u = \mathrm{f}(x) \text{ and}\hspace{0.5em} \frac{\mathrm{d}v}{\mathrm{d}x} = 1.\]
2. LIATE rule provides one of the ways to solve the integration, but it may not be the only way
3. 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 \(\displaystyle \displaystyle \displaystyle\int \sin^n x \, \mathrm{d}x\) (\(u = \sin^{n-1} x\))