Solve Indefinite Integral: 1/(x(sqrt(x^2 - 4)))

Click For Summary
SUMMARY

The integral of the function 1/(x(sqrt(x^2 - 4))) requires a trigonometric substitution for its solution. The discussion highlights the need for a substitution method, specifically suggesting the use of a trigonometric identity rather than a standard u-substitution. The user expresses confusion regarding the application of trigonometric substitutions, indicating a gap in their current calculus knowledge. The integral can be effectively solved using the substitution u = x/2, leading to a more manageable form.

PREREQUISITES
  • Understanding of basic integral calculus concepts
  • Familiarity with trigonometric identities and substitutions
  • Knowledge of u-substitution techniques
  • Experience with calculus at the BC level
NEXT STEPS
  • Study trigonometric substitution methods in integral calculus
  • Practice solving integrals involving square roots and rational functions
  • Review the concept of u-substitution and its applications
  • Explore advanced integration techniques covered in Calculus BC
USEFUL FOR

Students in Calculus BC, particularly those struggling with integration techniques, as well as educators looking for examples of trigonometric substitution in action.

sausu
Messages
2
Reaction score
0

Homework Statement



integral 1/(x(sqrt(x^2 - 4)))

Homework Equations



I don't know if there are any "equations" for integrals...


The Attempt at a Solution



Int(1/(x(Sqrt(4(x^2 /4)-1)
Int(1/(2x(Sqrt((x^2 /4)-1)
1/2 int(1/(x(Sqrt((x /2)^2)-1)
U-sub
u=x/2
du=1/2 dx
2du= dx
(This is where I hit a wall..I have no clue what I'm doing)
 
Physics news on Phys.org
For this one, you'll want to use a trig substitution instead of a regular u-substitution.
 
Bohrok said:
For this one, you'll want to use a trig substitution instead of a regular u-substitution.

We never learned how to do a trig substitution...
BTW I'm only in Calculus BC. We're just learning the basics of integrating.
 

Similar threads

  • · Replies 105 ·
4
Replies
105
Views
7K
  • · Replies 22 ·
Replies
22
Views
3K
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
9
Views
3K
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 27 ·
Replies
27
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K