Find ∫cosx dx\displaystyle\int \cos x\,dx∫cosxdx.
You may use the result ddx(tankx)=ksec2kx\dfrac{d}{dx}(\tan kx) = k\sec^2 kxdxd(tankx)=ksec2kx. Find ∫2sec24x dx\displaystyle\int 2\sec^2 4x\,dx∫2sec24xdx.
Hence, using the identity tan2θ≡sec2θ−1\tan^2\theta \equiv \sec^2\theta - 1tan2θ≡sec2θ−1, find ∫tan2θ dθ\displaystyle\int \tan^2\theta\,d\theta∫tan2θdθ.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.