Review question

How could we integrate $\tan^4x$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9297

Question

Given that $\dfrac{d}{dx}(\tan x)=\sec^2 x,$ differentiate $\tan^3x$ with respect to $x$.

Show that $\tan^4x=\tan^2x \sec^2x- \sec^2x+1$ and hence evaluate $\int_0^{\pi/4}\tan^4x \, dx.$