Question

Complete the table by identifying u and du for the integral (tan(x))^4(sec(x))^2

Answer 1

`\displaystyle (\tan^5x)/(5)+C`

Explanation:

`\displaystyle \int\tan^4x\sec^2x\,dx`

Let
`u=\tan x` and
`du=\sec^2x\,dx`:

`\displaystyle \int u^4\,du\\\\=(u^5)/(5)+C\\\\=(\tan^5x)/(5)+C`