What is the inetegral ln x?

The integral of ln(x) with respect to x is xln(x) - x + c, where c is an arbitrary constant. One can prove that this result is correct by using the method of integration by parts.

By setting u = ln(x) and v = x, one can use the integration by parts identity, which says that the integral of u with respect to v is equal to uv minus the integral of v with respect to u, to show that the integral of ln(x) is xln(x) - x + c. This method also uses the fact that the differential of ln(x) with respect to x is 1/x.