Changes

==Integration by Partial Fractions==

==Integration by Partial Fractions==

== 1st-Degree Denominators ==

== A 1st-Degree Denominator ==

These are a few methods of solving integrals with first degree denominators.

These are a few methods of solving integrals with first degree denominators.

=== 1st-Degree Denominator ===

=== A 1st-Degree Denominator ===

Given:

Given:

<br /><math>\int \frac{1}{ax + b}dx</math>

<br /><math>\int \frac{1}{ax + b}dx</math>

<br />The steps can be skipped by using the general formula above get:

<br />The steps can be skipped by using the general formula above get:

<br /><math>= \frac{8}{3} \ln{|3x+13|}+C</math>

<br /><math>= \frac{8}{3} \ln{|3x+13|}+C</math>

=== Repeated 1st-Degree Denominator ===

=== A Repeated 1st-Degree Denominator ===

The formula for integrals where a first degree polynomial denominator is raised to a power greater than one is much different than the formula above.

The formula for integrals where a first degree polynomial denominator is raised to a power greater than one is much different than the formula above.

Given

Given

<br /><math>= {-5 \over {(3)(12)(3x+17)^{11}}}+C = {-5 \over {36(3x+17)^{11}}}+C</math>

<br /><math>= {-5 \over {(3)(12)(3x+17)^{11}}}+C = {-5 \over {36(3x+17)^{11}}}+C</math>

== 2nd-Degree Denominators ==

== A 2nd-Degree Denominator ==

2nd-Degree Denominators get more complicated, especially with those that do not factor.

2nd-Degree Denominators get more complicated, especially with those that do not factor.

===Reducible 2nd-Degree Polynomial Denominator===

===A Reducible 2nd-Degree Polynomial Denominator===

:<big><math>\int\frac{3x+11}{x^2-x-6}dx</math></big>

:<big><math>\int\frac{3x+11}{x^2-x-6}dx</math></big>