Find the following indefinite integral:
\[
\int\left(36 x^{3}-18 x+15+\frac{17}{x}\right) d x
\]
$9 x^{4}-9 x^{2}+15 x+17 \ln |x|+c$
$12 x^{4}-18 x^{2}+15 x+17 \ln |x|+c$
$9 x^{4}-9 x^{2}+15 x+17 \ln |x|$
$12 x^{4}-18 x^{2}+15 x+17 \ln |x|$

Step 1 ：We are given the function \(36x^3 - 18x + 15 + \frac{17}{x}\) and we are asked to find its indefinite integral.

Step 2 ：We can integrate each term separately. The integral of a sum of functions is the sum of the integrals of the functions.

Step 3 ：The integral of \(x^n\) is \(\frac{1}{n+1}x^{n+1}\), the integral of a constant is the constant times \(x\), and the integral of \(\frac{1}{x}\) is \(\ln|x|\).

Step 4 ：Applying these rules, the integral of \(36x^3\) is \(9x^4\), the integral of \(-18x\) is \(-9x^2\), the integral of \(15\) is \(15x\), and the integral of \(\frac{17}{x}\) is \(17\ln|x|\).

Step 5 ：Adding these results together, we find that the indefinite integral of the function \(36x^3 - 18x + 15 + \frac{17}{x}\) is \(9x^4 - 9x^2 + 15x + 17\ln|x| + C\), where \(C\) is the constant of integration.

Step 6 ：Final Answer: The indefinite integral of the function \(36x^3 - 18x + 15 + \frac{17}{x}\) is \(\boxed{9x^4 - 9x^2 + 15x + 17\ln|x| + C}\)