Problem - 4552
Compute $$\int \ln{x} dx$$
This problem can be solved using substitution and integrate by part. Let $y=\ln{x}$, then $x=e^y$.
$$\int \ln{x} dx = \int y de^y = ye^y-\int e^ydy =ye^y - e^y + C =\boxed{ x\ln x - x +C} $$
Compute $$\int \ln{x} dx$$
This problem can be solved using substitution and integrate by part. Let $y=\ln{x}$, then $x=e^y$.
$$\int \ln{x} dx = \int y de^y = ye^y-\int e^ydy =ye^y - e^y + C =\boxed{ x\ln x - x +C} $$