The following denominator and trigonometric forms are provided in MF27. Match the integrand to the stated form and preserve its conditions.

Use trigonometric identities to rewrite the integrand as a standard or recognisable form.

MF27 denominator form	MF27 denominator form
\(\dfrac{1}{\sqrt{a^2-x^2}}\)	\(\dfrac{1}{a^2+x^2}\)
\(\dfrac{1}{a^2-x^2}\)	\(\dfrac{1}{x^2-a^2}\)

Source	Standard forms
Secondary level	\(\sin x,\ \cos x,\ \sec^2x,\ \mathrm{cosec}^2x\)
MF27	\(\tan x,\ \cot x,\ \mathrm{cosec}\,x,\ \sec x\)

Standard Integrals in MF27