Calculate the indefinite integral of ln(x)?

This would be calculated using the integration by parts method: NOTE: You can consider the function ln(x) to be a constant of value 1 multiplied by ln(x). The question would then become: Calculate the indefinite integral of : 1 * ln(x) The integration by parts method states: The integral of the product of two values u * (dv/dx) = u v - integral(v * (du/dx)). Using this we can assign u the value of ln(x) and (dv/dx) the value of 1. As we require du/dx we can differentiate ln(x) (aka u) to give 1/x. As we require v we can integrate 1 (aka dv/dx) with respect to x to give simply x. So: u = ln (x) v = x du/dx = 1/x dv/dx = 1 Then (using the original equation) the integral becomes: (ln(x) * x) - integral( x1/x ) = xln(x) - integral(1) + A [where A is a constant]. The integral of 1 is simply x so the answer is: xln(x) - x + C [where C is a constant] Note: The constant A is due to the 'by parts' section of the integral and can be ignored, as a second integral then takes place (integrating 1 in this case). Both of these constants are independent of x and therefore can be combined to give C.