Integrate (3x^2 - (1/4)x^-2 + 3) dx

3x²-(1/4)x^-2+3
Split the problem into three separate terms and integrate independently.With any term where x is to the power of something, divide the coefficient by the value of the power plus 1.e.g. 3x² ---> [3/(2+1)]x² ---> x²But this is not your final answer. You must then take the power and plus 1.x² ---> x²⁺¹ ---> x³
Applying this to the question:3x² ---> [3/(2+1)]x²⁺¹---> x³(1/4)x^-2 ---> [(1/4)/(-2+1)]x^-2+1 ---> (-1/4)x^-13 ---> 3x
Combined, this gives you:x³--(1/4)x^-1+3x+C= x³+(1/4)x^-1+3x+C