How would I integrate the indefinite integral x^2 dx?

Remember the rule for integrating is that x^n integrates to xⁿ⁺¹/(n+1). Here, n = 2 so n+1 = 3. Therefore the integral will be (x³)/3. Remember that as the integral has is indefinite- it has no limits- you have to add a constant which is denoted by + c. The overall answer therefore is (x³)/3 + c.