Final answer:
The integral of (x³-7)/x is found by simplifying the expression to x²-7/x and then integrating each term to get (1/3)x³ - 7 ln|x| + C, where C is the constant of integration.
Step-by-step explanation:
When finding the integral of the function (x³-7)/x, we first simplify the expression inside the integral. This can be done by dividing both terms by x which gives us x²-7/x. We then integrate each term separately.
∫ (x³-7)/x dx = ∫ x² dx - ∫ 7/x dx
The integral of x² is (1/3)x³ and the integral of 7/x is 7 ln|x|. So, the integral of the original function is:
∫ (x³-7)/x dx = (1/3)x³ - 7 ln|x| + C
where C is the constant of integration.