How Do You Integrate the Square Root of Tan x?

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SUMMARY

The integral of the square root of tan x, represented as \int \sqrt{\tan x} \; dx, can be approached by substituting u = \sqrt{\tan x}, leading to a rational integrand suitable for partial fraction decomposition. The discussion highlights the importance of correctly changing variables, as neglecting to adjust dx to du can lead to incorrect results. Various users shared their experiences and methods, including references to elliptic integrals and the use of tools like Mathematica for verification.

PREREQUISITES
  • Understanding of integral calculus, specifically substitution methods.
  • Familiarity with trigonometric functions and their properties.
  • Knowledge of partial fraction decomposition techniques.
  • Basic understanding of elliptic integrals and their applications.
NEXT STEPS
  • Study the substitution method in integration, focusing on trigonometric functions.
  • Learn about elliptic integrals and their significance in calculus.
  • Explore the use of Mathematica for solving complex integrals.
  • Investigate partial fraction decomposition in greater detail.
USEFUL FOR

Calculus students, mathematics educators, and anyone interested in advanced integration techniques involving trigonometric functions.

  • #31
At any rate, it is a fairly easy integral. Two subtitutions and a partial fraction decomposition will give the answer. It's messy though, much neater to do a definite integral working out the substitutions along the way.
 
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  • #32
Orion1 said:
I understand, a CalcI student should use the Data Denominator Theorem.

Data Denominator Theorem:
\int \frac{1}{u(x)}} dx = F(x) + C
[/Color]
"Data Denominator Theorem" ?! Did you invent that? It makes no sense to me at all.
 
  • #33
TD said:
"Data Denominator Theorem" ?! Did you invent that? It makes no sense to me at all.
Of course he did. :biggrin: :approve:
 
  • #34
Jeremy said:
My class, teacher included, cannot seem to figure out the integral of the square root of tan x. Maybe someone here can help?

thanks,
jeremy

it is not easy n also very lenthy n time taking
 
  • #35
http://math.ucsd.edu/~wgarner/math10b/int_sqrt_tan.htm
 
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  • #36
hope someone can figure out the integral sqrt(tanx)...
 
  • #37
soccer*star said:
http://math.ucsd.edu/~wgarner/math10b/int_sqrt_tan.htm

it helps a lot...:wink:
 
Last edited by a moderator:

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