H2 Math Integration Techniques Every JC Student Must Know

Integration accounts for a significant portion of H2 Mathematics marks and is one of the topics where students can gain or lose the most marks. There are 6 main integration techniques tested at A-Level, and knowing when to apply each one is as important as knowing how to execute it.

Technique 1: Standard Results (Must Memorise)

• ✓∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1)
• ✓∫1/x dx = ln|x| + C
• ✓∫eˣ dx = eˣ + C
• ✓∫sin x dx = -cos x + C
• ✓∫cos x dx = sin x + C
• ✓∫sec²x dx = tan x + C
• ✓∫1/(1+x²) dx = arctan x + C

Technique 2: Integration by Substitution

Use substitution when you can identify a function and its derivative within the integrand. Let u = the inner function, find du/dx, substitute, integrate with respect to u, then substitute back. The key skill is recognising which substitution to use — this comes with practice.

Technique 3: Integration by Parts

∫u dv = uv - ∫v du. Choose u using LIATE (Logarithm, Inverse trig, Algebraic, Trigonometric, Exponential). The function higher in the list should be u. Sometimes you need to apply integration by parts twice — this is common for ∫x²eˣ dx and ∫eˣ sin x dx.

Technique 4: Partial Fractions

Use partial fractions when integrating rational functions where the denominator can be factored. Decompose the fraction into simpler fractions, then integrate each term separately. Remember: for a repeated linear factor (x-a)², you need two terms: A/(x-a) + B/(x-a)².

Technique 5: Trigonometric Identities

For integrals involving sin²x or cos²x, use the double angle formulae: sin²x = (1 - cos 2x)/2 and cos²x = (1 + cos 2x)/2. For products like sin x cos x, use sin 2x = 2 sin x cos x.