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A hint to get started

Recognise arcsine and arctangent forms

Integrate with respect to xx: (a) 14−x2\frac1{\sqrt{4-x^2}}; (b) 19+x2\frac1{9+x^2}; (c) 11−4x2\frac1{\sqrt{1-4x^2}}. For (c), compare the MF27 formula with the general composite formula.

CJC · Lecture · Example 5

For a basic form, the Teacher emphasises numerator 1 and coefficient of the squared variable 1.

For a composite form, supply its derivative with a compensating factor. The highlighted domain condition is |f(x)|<a.

Read the worked solution