$$\log_{10}\left(x\right)+\log_{10}\left(x+12\right)=\log_{10}\left(x-10\right)$$

$$\left(\frac{x^2}{x^2-x+42}\right)-\left(\frac{36}{x^2-x+42}\right)$$

$$\int_1^3\left(\frac{2x^3+10x-1}{x^2+5}\right)dx$$

$$\sqrt[3]{a^2\sqrt[3]{a}}$$

$$\frac{d\eta\left(t\right)}{dt}=\frac{\exp\left(t\right)}{\eta}$$

$$\frac{d}{dx}\left(y^2=x^{x^2}\right)$$

$$x^2+4x+4\ge0$$