Solve 1/4x^2(2lnx-1)-operatorname{ax}(lnx+1)-1/2x^4

$$\frac { 1 } { 4 } x ^ { 2 } ( 2 \ln x - 1 ) - \operatorname { ax } ( \ln x + 1 ) - \frac { 1 } { 2 } x ^ { 4 }$$

Factor

$$\frac{x\left(x\left(2\ln(x)-1\right)-4a\left(\ln(x)+1\right)-2x^{3}\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{2}\left(2\ln(x)-1\right)-4ax\left(\ln(x)+1\right)-2x^{4}}{4}$$

Consider x^{2}\left(2\ln(x)-1\right)-4ax\left(\ln(x)+1\right)-2x^{4}. Factor out x.

$$x\left(x\left(2\ln(x)-1\right)-4a\left(\ln(x)+1\right)-2x^{3}\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(x\left(2\ln(x)-1\right)-4a\left(\ln(x)+1\right)-2x^{3}\right)}{4}$$

Evaluate

$$\frac{x\left(x\left(2\ln(x)-1\right)-4a\left(\ln(x)+1\right)-2x^{3}\right)}{4}$$