Question

Integrate (6x^2-cos(2x))dx??

Answer 1

Using the "Just look at it Theorem"

Integral (6x^2 - cos(2x) dx
= 2x^3 - (1/2)sin(2x) + constant

you can easily check by mentally finding the derivative of the above answer

Answer 2

That's my favorite theorem! Too bad it's not taught more.

In all fairness, when you're brand new at this stuff, things often seem more confusing than they are.

The main problem I encounter is that students seem to forget what the exercise set covers. If you've just been studying integration of powers and trig functions, it's not likely that the problems will branch out into strange territory.

Same thing with word problems. Read the story -- it will almost always produce an equation just like those you just worked in the previous section of exercises!!!