Question

Note: This is NOT a question. This is a tutorial.

How to do basic integration? See comments below for a tutorial on the more basic concepts of integration.

Answer 1

Continued from
http://openstudy.com/study#/updates/4f9d495be4b000ae9ed1ecba

Answer 2

We shall start with some rules that will help us integrate more basic functions. All of these rules are actually counterparts of their differentiation rules. Shamelessly ripped off from @lgbasallote 's guide on basic derivatives, as well as my textbook.

Rule: d/dx ax^n=nax^(n-1)
Counterpart:∫ax^n dx = (ax^(n+1))/(n+1)+C

Rule: d/dx ln x=1/x
Counterpart: ∫ 1/x dx=ln |x|+C

Trig functions coming up next.

Answer 3

Rule: d/dx sin(x)=cos(x)
Counterpart: ∫ cos(x) dx= sin(x)+C

Rule: d/dx cos(x)=-sin(x)
Counterpart: ∫ sin(x) dx=-cos(x)+C

Rule: d/dx tan(x)=sec^2 (x)
Counterpart: ∫ sec^2 (x)=tan(x)+C

The derivatives and counterparts of the other trig functions can be found by using the product rule or quotient rule. Note that we do not yet have ways to find the indefinite integrals of certain trigonometric functions, such as sec(x) or tan(x).

Answer 4

We spend much less time discussing the indefinite integrals of polynomial functions as opposed to in differential calculus, because it is unnecessary. When finding the anti-derivative of a function, there are two main ways, which are "counterparts" of the Chain Rule and Product Rule. These are commonly called integration by u-substitution, and integration by parts, respectively.