$$\frac{dy}{dx}=\frac{1}{6x-42}$$

$$\int_{-1}^2\frac{3x}{x+4}dx$$

$$\int_9^4\left(\frac{x^2}{x+1}\right)dx$$

$$\int_e^{\infty}\left(\frac{1}{x\left(\ln\left(x\right)\right)^3}\right)dx$$

$$\int_2^{\infty}\left(\frac{lnx}{x}\right)dx$$

$$\int_1^{25}\frac{\left(\left(lnx\right)^5\right)}{4x}dx$$