find the indefinite integral of the following g(x)=21-12x^3/x (x>0)
To find the indefinite integral of g(x) = (21 - 12x^3) / x (x > 0), we can follow these steps:
Step 1: Separate the terms
You can rewrite g(x) as: 21/x - 12x^2/x
Step 2: Simplify the terms
The first term, 21/x, can be integrated as (21 ln|x|) + C, where C is the constant of integration.
The second term, 12x^2/x, simplifies to 12x.
Step 3: Combine the results
Adding up the two results, we get the indefinite integral of g(x) as:
(21 ln|x|) + 12x + C, where C is the constant of integration.
So, the indefinite integral of g(x) is (21 ln|x|) + 12x + C.