Solve f(x)=xlnx+x^2ln^3x/x^2lnx

$$f ( x ) = \frac { x \ln x + x ^ { 2 } \ln ^ { 3 } x } { x ^ { 2 } \ln x }$$

Evaluate

$$3+\frac{1}{x}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{\ln(e)}x\left(x\ln(x^{3})+\ln(x)\right)}{\frac{1}{\ln(e)}x^{2}\ln(x)}$$

Cancel out \frac{1}{\ln(e)}x in both numerator and denominator.

$$\frac{x\ln(x^{3})+\ln(x)}{x\ln(x)}$$

Expand the expression.

$$\frac{3x\ln(x)+\ln(x)}{x\ln(x)}$$

Factor the expressions that are not already factored.

$$\frac{\left(3x+1\right)\ln(x)}{x\ln(x)}$$

Cancel out \ln(x) in both numerator and denominator.

$$\frac{3x+1}{x}$$

Factor

$$\frac{3x+1}{x}$$