Find the general antiderivative of $n(x)=\frac{x^{9}+5 x^{3}}{x^{4}}$. Use $C$ for the arbitrary constant. (If necessary, rewrite the function before antidifferentiation.) Answer

Step 1 ：Given the function \(n(x)=\frac{x^{9}+5 x^{3}}{x^{4}}\), we first simplify it by dividing each term in the numerator by \(x^{4}\).

Step 2 ：This simplifies the function to \(x^{5} + 5x^{-1}\).

Step 3 ：We then find the antiderivative of each term separately. The antiderivative of \(x^{5}\) is \(\frac{1}{6}x^{6}\) and the antiderivative of \(5x^{-1}\) is \(5\ln|x|\).

Step 4 ：Combining these, the general antiderivative of \(n(x)=\frac{x^{9}+5 x^{3}}{x^{4}}\) is \(\boxed{\frac{1}{6}x^{6} + 5\ln|x| + C}\).