Find the indefinite integral of x^8*ln(3x) using integration by parts

For this method we need to choose our u and dv/dx. Using the Late method (Logarithm, algebra, trigonometric, exponential), we can pick our u value which will be ln(3x). du/dx is therefore 1/x, using the chain rule. dv/dx = x^8, therefore v = (x^9)/9. Using the integration by parts formula, which is u*v - int[(du/dx)v] which equals (x^9/81)(9ln(3x)-1) + C, where C is a constant of integration