Integration Techniques Final

Integration Techniques

Are divided in 3

Double substitution/ Change of variable

Partial Fractions

Integration by Parts

First we need to arrange the function if there is a root

Arrange the x alone (in terms of "u")

Example

Is always a fraction

We need to factorize the denominator

After we factorize, we will split the equation

Each letter corresponds to a part of the factorized denominator

If we have a term with an exponent, it needs to be placed in different letters.

Example

Sergio Figueroa A01173360

Used when we cannot cancel anything

Used when we have "ln"

Instead of double substitution

To use this formula we need to locate the "u" using LATE

Logarithmic

Algebraic

Trigonometric

Exponential

"u" is located following this pattern, the one who is first is the "u" depending on the equation

Example

Take out "du" and "dx"

Replace the x in the function and integrate

Tabular method

Is a shortcut to solve integration by parts

Cases we can use tabular method

We use a table to arrange the equations

We derivate "u" until we get to 0

Table

We derivate de "u" obtained by LATE until 0

Function evaluated

After we derivate "u" and integrate "dv", we use the arrows to get the final answer (diagonals)

Final answer