Integrate 8x^3+4 with respect to x.

We can compute this integral in two parts: we integrate (8x^3) first then integrate 4, and reach our final answer be adding together our two results. Integrating 4 is the easiest as 4 is just a constant - hence we get 4x by increasing the power of x by 1. To integrate (8x^3), we first increase the power of x by 1 to get (x^4), then we need to find a constant 'a' such that 4*a=8. Hence a=2. So the integral of (8x^3) is (2x^4). Adding our two results together gives (2x^4+4x) and, as this is an indefinite integral (there are no bounds on it), we must add a constant c on the end. Hence our final solution is (2x^4+4x+c). We can check this result by differentiating it to see if we get the equation in the question.