Find $\int 2^{x}dx$.

A factory consumes electricity at a rate of $1500\text{ MJ}$ per year at $t=0$ years. The consumption rate increases by $2.1\%$ per year. Determine the function for total energy consumed by the factory (in units of $\text{MJ}$) between $t=0$ and $t$ years.

Evaluate the integral: ${\int }_0^{\ln 4}\frac{e^x-e^{-x}}{e^x+e^{-x}}dx$

Evaluate the area under the curve $y=\frac{2}{x}$ between $x=1$ and $x=e^2$.

Evaluate the integral: $\int \frac{x+3}{x^2+6x+10}dx$

Find the integral: $\int \frac{\sqrt{9-(\ln x{)}^2}}{x\ln x}dx$