Integration by recognition and trigonometric identitiesEdexcel International A Level Maths: Mind map

Exam questions on Integration by recognition and trigonometric identities

1. The function $h$ is defined by $h(x)=\frac{x}{x^2+5}$ for $x\geq0$.
   Find $\int\frac{x}{(x^2+5)^2}\,dx$.2 marks
2. The function $f$ is defined by $f(x)=\tan x$ for $0\leq x<\frac{\pi}{2}$.
   Find $\int[f(x)]^2\,dx$.2 marks
3. The curves $C_1$ and $C_2$ have equations $y=\cos^23x$ and $y=\sin^23x$ respectively, for $0\leq x\leq\frac{\pi}{12}$.
   Show that $\cos^23x=\frac12(1+\cos6x)$, and hence find $\int\cos^23x\,dx$.3 marks