$$\int\left(x^2+x-2\right)e^{2x}\:dx$$

$$4x^2+24x+27$$

$$\lim_{x\to0}\left(4+x^{3lnx}\right)$$

$$_{\left(x-y\right)}dx\:+x\:dy=0$$

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

$$ydx+\left(3x+4y\right)dy=0$$

$$1-\sec\left(x\right)+\tan\left(x\right)$$