How Do You Integrate 1/(1+a*cos(x))?

  • Thread starter Thread starter tennishaha
  • Start date Start date
  • Tags Tags
    Integrating
Click For Summary

SUMMARY

The integral of the function 1/(1+a*cos(x)) can be efficiently computed using Wolfram Alpha, as manual calculation involves complex integration by parts and the inverse hyperbolic tangent function. The substitution t = tan(θ/2) is recommended as a standard technique to simplify the integration process. While some may view using computational tools as cheating, it is a practical approach to avoid unnecessary complexity in calculations.

PREREQUISITES

  • Understanding of integral calculus
  • Familiarity with integration techniques, particularly integration by parts
  • Knowledge of hyperbolic functions and their properties
  • Experience using computational tools like Wolfram Alpha

NEXT STEPS

  • Research the application of the substitution method t = tan(θ/2) in integrals
  • Explore advanced integration techniques involving inverse hyperbolic functions
  • Learn how to use Wolfram Alpha for complex integral calculations
  • Study the properties and applications of hyperbolic functions in calculus

USEFUL FOR

Students and educators in mathematics, particularly those studying calculus and integral techniques, as well as anyone seeking efficient methods for solving complex integrals.

tennishaha
Messages
21
Reaction score
0

Homework Statement



How to integral this one?

1/(1+a*cosx)



Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
In this case, you use wolframalpha.com because the calculation by hand is brutal.

http://www.wolframalpha.com/input/?i=integrate+(1%2Ba*cos(x))^-1

Some people think that's cheating, but I think doing the grunt work here would be a waste of time since there's no new insight. From the looks of it, it's just several cumbersome integration by parts with the inverse hyperbolic tangent function.
 
I would try [tex]t=\tan (\theta /2)[/tex], it's one of the standard ones.
 

Similar threads

Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
Integrating 1/(1+cosx) from -pi/2 to pi/2
  • · Replies 5 ·
Replies
5
Views
2K
What are the units of the argument "x" for this cos(x) function integral?
  • · Replies 7 ·
Replies
7
Views
2K
Integration problem ∫sqroot((cosx-cos^3(x))/(1-cos^3(x)))
  • · Replies 18 ·
Replies
18
Views
2K
Integration problem ∫1/(√3 sinx+ cosx) dx
  • · Replies 8 ·
Replies
8
Views
2K
Integrate 4cos(x/2)cos(x)sin(21x/2) Homework
  • · Replies 2 ·
Replies
2
Views
3K
Integral of 1 / (x^2 + 2) dx ?
  • · Replies 54 ·
2
Replies
54
Views
20K
Double Integral of function in region bounded by two circles
  • · Replies 19 ·
Replies
19
Views
4K
Evaluate the integral: ∫csc((v-π)/2)cot((v-π)/2)
  • · Replies 3 ·
Replies
3
Views
3K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
3K