Technique selection process for integration.
Techniques of Integration — H2 Mathematics
Standard Integrals from Sec Level
Recognisable Form (Cancelling Method)
Integration of Algebraic fractions
\(\int\dfrac{\mathrm{f}(x)}{\mathrm{g}(x)}\,\mathrm{d}x\quad\text{or}\quad\int\dfrac{\mathrm{f}(x)}{\sqrt{\mathrm{g}(x)}}\,\mathrm{d}x\)
Do long division if the degree of \(\mathrm{f}(x)\) is at least the degree of \(\mathrm{g}(x)\). If \(\mathrm{f}(x)\) is a constant and \(\mathrm{g}(x)\) is quadratic, complete the square of \(\mathrm{g}(x)\), then use the integrals of If \(\mathrm{g}(x)\) can be factorised, express \(\dfrac{\mathrm{f}(x)}{\mathrm{g}(x)}\) in partial fractions and integrate. Lastly, if steps 1–3 are exhausted, consider “Split Up Method”.
Trigonometric Functions Use trigonometric identities and change to integrable trigonometric forms or cancelling method. There are 8 trigonometric integrable forms:
\(\sin x,\ \cos x,\ \sec^2x,\ \operatorname{cosec}^2x\) [From Sec Level]
\(\tan x,\ \cot x,\ \operatorname{cosec}x,\ \sec x\) [From MF 27]
Integration by parts
\(\int u\dfrac{\mathrm{d}v}{\mathrm{d}x}\,\mathrm{d}x=uv-\int v\dfrac{\mathrm{d}u}{\mathrm{d}x}\,\mathrm{d}x\)
