Activity 5.3.4

Evaluate each of the following definite integrals exactly through an appropriate $u$-substitution.

1. $\displaystyle \int_1^2 \frac{x}{1 + 4x^2} \, dx$

2. $\displaystyle \int_0^1 e^{-x} (2e^{-x}+3)^{9} \, dx$

3. $\displaystyle \int_{2/\pi}^{4/\pi} \frac{\cos\left(\frac{1}{x}\right)}{x^{2}} \,dx$