It looks like you've uploaded a file with a set of integral problems. Would you like me to walk through each of them step by step? Let me know if you'd prefer explanations or if you'd like a quick solution for any of the specific integrals.

Here's a quick breakdown of the problems:

1. Problem 2: $\int \frac{dx}{(x^2 + 25)^{3/2}}$
2. Problem 3: $\int_1^\infty \frac{x}{(x^2 + 1)^2} dx$
3. Problem 4: $\int_1^\infty \frac{1}{(x^2 + 1)^2} dx$
4. Problem 5: $\int_0^{\frac{\pi}{2}} \sin^3(x) \cos^3(x) dx$
5. Problem 6: $\int x \cot(x) \csc(x) dx$

Would you like me to start solving them one by one?