Question

How do you integrate `int x(x^2+3)dx`?

Answer 1

`intx(x^2+3)dx=1/4(x^2+3)^2+C`

Explanation:

It can be done by other methods, but if you recognise that the `x` outside the bracket results from the bracket differentiated we can integrate by inspection.

now `d/(dx)((x^2+3)^2)=2xx2x(x^2+3)=4x(x^2+3)`

Thus `intx(x^2+3)dx=1/4(x^2+3)^2+C`