Can a Simple Integral Solve 1/(K + x^2)^(3/2)?

  • Thread starter Thread starter Mattofix
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
SUMMARY

The integral of 1/(K + x^2)^(3/2) can be solved using hyperbolic or trigonometric substitutions. The discussion highlights two effective methods: the substitution x = √K sinh(u) favored by arildno, and the alternative substitution x = √K tan(θ) preferred by another participant. Both approaches are valid and yield the same result, demonstrating the flexibility in solving integrals of this form.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with hyperbolic functions
  • Knowledge of trigonometric identities
  • Experience with substitution methods in integration
NEXT STEPS
  • Study hyperbolic substitution techniques in integration
  • Learn about trigonometric substitution methods for integrals
  • Explore advanced integral calculus topics
  • Practice solving integrals involving rational functions
USEFUL FOR

Students and educators in calculus, mathematicians interested in integration techniques, and anyone looking to enhance their problem-solving skills in integral calculus.

Mattofix
Messages
137
Reaction score
0
A simple integral?!?

Homework Statement



Integrate 1/(K+ x^2)^(3/2) dx

Homework Equations





The Attempt at a Solution



substitution of some kind - if it had an x on top it would be fine...
 
Physics news on Phys.org
Set x=\sqrt{K}Sinh(u) and proceed.
 
arildno loves that hyperbolic substitution!

Myself, I would have immediately thought that "tan^2(\theta)+ 1= sec^2(\theta)" and used the substitution x= \sqrt{K}tan(\theta). I suspect it is just a matter of taste.
 

Similar threads

Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
4
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
7
Views
2K
  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 44 ·
2
Replies
44
Views
6K
Replies
9
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 54 ·
2
Replies
54
Views
16K