1. Take the derivative of each complex part in the question. For example, the question 2 in assignment 3, the derivative of cos(t) is -sin(t). There is a sin(t) over cos^2(t), which seems to substitute cos(t). As well, if there is cos(x^3), it is reasonable to take the derivative of x^3 first.

2. Be sensitive when you see a number or expression. In Wednesday class, there is a question which ask to evaluate the integral of x^3cos(x^2)dx from 0 to square root of pi. Except the first tip, there is a square root of pi, which is a little bit complicated. It is easiest way to simplify it to square it, which turn it to pi. In this case, it seems to substitute x^2.

3. If there is a question asking to calculate the integral of x^2*sin(x^2+4), always substitute x^2+4 which is a part of sin. In this way, the derivative of x^2 and x^2+4 is identical, but it is much easier if we substitute x^2+4.

4. Memorize the formulae. If a question is same as the pattern of a formula, try to transform it to the formula by substitution, just like the question 2b in assignment 3.