find the most general antiderivative or indefinite integral. ∫9x(7 - x^(-4))dx ∫9x(7 - x^(-4))dx = □

Explanation:

Step1: Expand the integrand

$9x(7 - x^{-4})=63x - 9x^{-3}$

Step2: Integrate term - by - term

$\int(63x - 9x^{-3})dx=\int63x dx-\int9x^{-3}dx$ Using the power rule for integration $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), we have: $\int63x dx=63\times\frac{x^{1 + 1}}{1+1}=\frac{63}{2}x^{2}$ $\int9x^{-3}dx=9\times\frac{x^{-3 + 1}}{-3 + 1}=-\frac{9}{2}x^{-2}$

Step3: Combine the results

$\int(63x - 9x^{-3})dx=\frac{63}{2}x^{2}+\frac{9}{2x^{2}}+C$

Answer:

$\frac{63}{2}x^{2}+\frac{9}{2x^{2}}+C$