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.