$$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$$

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

$$\int_1^2x\ln\left(x\right)dx$$

$$\int_0^{\infty}\left(1+2x\right)e^{-x}dx$$

$$\int_1^{\infty}\left(\frac{ln\:x}{x^2}\right)dx$$

$$\int_0^1xlnxdx$$

$$\int_0^1x\ln\left(x\right)dx$$