Integrate x((x^2)+2) dx

The first step is to multiply out the brackets so the function is in a form that can be integrated. X x X² = X³ then X x 2 is simply 2X. So we are left with X³ + 2X. Both parts of this function can be integrated normally by rising the power by one and then dividing the coefficient by the new power. So 3+1=4 then divide the coefficient (1) by  4 gives us 1/4(X⁴) . Doing the same with 2X gives us x². We can differentiate this two parts to double check we have integrated properly. The last step is to add a constant i.e. +C, as no limits were given in the question,