Answer
$$4{x^4} - 5x\ln x + 5x + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {12{x^2} - 5\ln x} \right)} dx \cr
& {\text{sum rule for derivatives}} \cr
& = \int {12{x^2}} dx - \int {5\ln x} dx \cr
& {\text{use the constant multiple rule }}\int {kf\left( x \right)dx} = k\int {f\left( x \right)} dx \cr
& = 12\int {{x^2}} dx - 5\int {\ln x} dx \cr
& \cr
& {\text{Integrate using the rules of integration}} \cr
& \int {\ln x} dx = x\ln x - x + C,\,\,\,\,\int {{x^r}} dx = \frac{{{x^{r + 1}}}}{{r + 1}} + C \cr
& \cr
& = 12\left( {\frac{{{x^3}}}{3}} \right) - 5\left( {x\ln x - x} \right) + C \cr
& {\text{simplifying}} \cr
& = 4{x^4} - 5x\ln x + 5x + C \cr} $$
