a) Find the indefinite integral of sec^2(3x) with respect to x. b) Using integration by parts, or otherwise, find the indefinite integral of x*sec^2(3x) with respect to x.

a) First deduce that problem can be solved by inspection. Then use the fact that the derivative of tan3x equals 3sec^2(3x) and adjust for the constant. (Note this fact should be given in a formula booklet).b) Decide which part of the expression you will differentiate and which part you will integrate (note part a of the questions asks you to integrate something so this is a big hint. You can also use acronym LIATE). Use integration by parts formula which should also be given but it is handy to memorize it. Work carefully through algebra. (Note I will write the math on the whiteboard).