Answer:
= ax + b ln x - c/x + C
Step-by-step explanation:
Recall:
integral a dx = ax + C
integral 1/x dx = ln x + C
integral x^(n) = [x^(n +1)]/(n + 1) + C
Also:
c = variable in this problem
C = constant you add when you integrate
Separate each term of the numerator and set it over the denominator.
integral (ax^2 + bx + c)/x^2 dx =
integral [(ax^2)/x^2 + (bx)/x^2 + c/x^2] dx
Simplify each term and separate into the sum of 3 integrals.
= integral (a dx) + integral (b/x dx) + integral (c/x^-2) dx
= ax + b ln x + (cx^-1)/(-1) + C
= ax + b ln x - c/x + C
