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
