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Topic 1: Integration techniques

Integration techniques

10 hours

• Integrate using the trigonometric identities sin²(x) = ½(1 − cos(2x)), cos²(x) = ½(1 + cos(2x)), 1 + tan²(x) = sec²(x) and cot²(x) + 1 = cosec²(x).
• Establish and use the formula ∫ sec²(x) dx = tan(x) + c.
• Use substitution u = g(x) to integrate expressions of the form f(g(x)) g′(x).
• Establish and use the formula ∫ (1/x) dx = ln|x| + c for x ≠ 0 and ∫ (f′(x)/f(x)) dx = ln|f(x)| + c for f(x) ≠ 0.
• Understand and use the inverse trigonometric functions: arcsine, arccosine and arctangent. 1 interactive
• Use the derivative of the inverse trigonometric functions: arcsine, arccosine and arctangent.
• Integrate expressions of the form ±1/√(a² − x²) and 1/(a² + x²).
• Use partial fractions for integration involving two distinct linear factors in the denominator, e.g. (2x − 1)/((x + 1)(x − 2)). 1 interactive
• Integrate by parts. 1 interactive