Part 1

1. Integrate and simplify your result.
   
   $$\int_{0}^{\pi/3} \cos^4 t \sin^2 t dt$$
   
   

2. Integrate
   
   $$\int \frac{dx}{x^2\sqrt{9-x^2} }$$
   
   

3. Integrate
   
   $$\int \frac{1}{x^2(x^2+4)} dx$$
   
   

4. Determine if the following integral converges or diverges, and evaluate the integral if it converges.
   
   $$\int_{0}^{\infty} x^2 e^{-x^3} dx$$