It looks like you've uploaded an image of a math assignment. Here's a breakdown of the questions visible:

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

2. Integrate
   $\int \frac{x \, dx}{(x - a)^2 (x - b)}$ (4 Marks)

3. Obtain a reduction formula for
   $\int (x^2 + a^2)^n dx$ (3 Marks)

4. Evaluate from first principle
   $\frac{d}{dx} \left( e^x \right)$ (3 Marks)

5. Evaluate
   $\lim_{n \to \infty} \left( \left(1 + \frac{1}{n}\right) \left(1 + \frac{2}{n}\right) \cdots \left(1 + \frac{n}{n}\right) \right)^{\frac{1}{n}}$ (3 Marks)

6. Evaluate, if possible
   $\int_{-\infty}^{\infty} \frac{dx}{1 + x^2}$ (4 Marks)

Would you like a step-by-step solution for a particular question, or should I solve them one by one? Let me know!

Here are some related questions to help further your understanding:

1. How would you approach integration by parts for complex integrals?
2. What techniques are useful when handling improper integrals?
3. What is the concept behind a reduction formula in integration?
4. How do you interpret limits involving infinite products?
5. Why is the derivative of $e^x$ the same as the function itself?

Tip: For integrals, always consider whether substitution, partial fractions, or other standard methods apply before moving to more advanced techniques.