• Support PF! Buy your school textbooks, materials and every day products Here!

Trig Integration

  • Thread starter Aerosion
  • Start date
  • #1
53
0

Homework Statement



[tex]\int_\frac{dx}{(4+x^2)^2}dx[/tex]

Homework Equations





The Attempt at a Solution



SO....I started by making [tex]x = 2*tan x[/tex] and [tex]dx = 2*sec(x)^2[/tex]. The x is supposed to be the 0 sign with the line through it, but I don't know how to make that.

I then made the equation [tex]\int \frac{2*sec(x)^2}{(4+2*tan(x)^2}*2*sec(x)^2[/tex]. I multiplied the two secants to get [tex]4*sec(x)^4[/tex] on the top, and then I turned the [tex]2*tan(x)^2[/tex] on the bottom into [tex]2*sec(x)^2-2[/tex]. The equation now looks like [tex]\int \frac{4*sec(x)^4}{(4+2*sec(x)^2-2}[/tex]. How does this simplify? I want to get rid of the [/tex]2*sec(x)^2[/tex] by dividing it with the top thing, but I don't think I can do that becaause of the -2 attached to it.
 
Last edited:

Answers and Replies

  • #2
you should fix your latex formatting.

your integral becomes cos²(x).

Show your work again, and let us know if you get stuck.
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
12,981
540
[tex] \int \left(\frac{1}{-2x}\right)\left(\frac{-2x}{(4+x^2)^2}{}dx\right)=-\frac{1}{2x}\cdot\frac{1}{4+x^2}+\frac{1}{2}\int \frac{dx}{x^2 (4+x^2)} [/tex]

[tex] =-\frac{1}{2x}\cdot\frac{1}{4+x^2}+\frac{1}{8}\int \left(\frac{1}{x^2}-\frac{1}{4+x^2}\right){}dx [/tex]

...
 

Related Threads on Trig Integration

  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
2
Views
669
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
893
  • Last Post
Replies
2
Views
1K
Top