Question

How do you integrate by substitution `int t^2(t-2/t)dt`?

Answer 1

`((t^2-2)^2)/4+C`

Explanation:

`intt^2(t-2/t)dt`
`intt(t^2-2)dt`

Substitute `u=t^2-2` , `(du)/(dx) =2t`

`1/2int2t(t^2-2)dt`
`1/2int(u)du`
`1/2((u^2)/2)`
`(u^2)/4`

Undo substitution:
`((t^2-2)^2)/4+C`