How Do You Integrate 1/((x-1) sqrt(x^2-2x+5))?

  • Context: Graduate 
  • Thread starter Thread starter worstcalcbook
  • Start date Start date
  • Tags Tags
    Integrate
Click For Summary
SUMMARY

The integration of the function 1/((x-1) sqrt(x^2-2x+5)) presents significant challenges, as noted in the discussion. The user attempted to utilize Wolfram Alpha for assistance but found it inadequate for this specific problem. Key substitutions mentioned include s = arctan(u/2) and u = 2 tan(x), which were not thoroughly explained in the user's reference materials. Ultimately, the user resolved the issue independently, highlighting the limitations of automated tools in complex integration scenarios.

PREREQUISITES
  • Understanding of integral calculus and substitution methods.
  • Familiarity with trigonometric identities and substitutions.
  • Knowledge of Wolfram Alpha and its capabilities for mathematical problems.
  • Experience with algebraic manipulation involving square roots and rational functions.
NEXT STEPS
  • Explore advanced integration techniques, particularly trigonometric substitutions.
  • Study the use of Wolfram Alpha for complex calculus problems and its limitations.
  • Learn about the derivation and application of the arctan substitution in integrals.
  • Investigate alternative mathematical software for solving integrals, such as Mathematica or MATLAB.
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus, as well as educators seeking to understand common pitfalls in teaching integration techniques.

worstcalcbook
Messages
2
Reaction score
0
http://www.wolframalpha.com/input/?i=integrate+1%2F%28%28x-1%29+sqrt%28x^2-2x%2B5%29%29

I have this problem, but there's no solution for it although it's definitively the hardest (people who lack common sense shouldn't write manuals). So, I decided to use wolfram, but it doesn't really help. I don't know how to substitute back s = arctan (u/2) without getting blood on my hands and have no idea where that u = 2 tan x substitution comes from because it wasn't covered in the book. There's only a substitution that's similar (u = tan (x/2)), but I digress.
 
Physics news on Phys.org
Nevermind, solved it. Wolfram Alpha is useless most of the time.
 

Similar threads

Undergrad Troubleshooting a difficult integral
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Integration of the Maxwell Speed Distribution
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad How Do You Integrate Expressions Like These?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?
  • · Replies 8 ·
Replies
8
Views
2K
MHB What is the integral of $\frac{x^2-1}{\sqrt{2x-1}}$?
  • · Replies 5 ·
Replies
5
Views
2K
MHB What is the correct solution for $\int_{0}^{1}x\sqrt{18-2x^2} \,dx$?
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the integral of $\sqrt{x^2-1}$? What is the integral of $\sqrt{x^2-1}$?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Why Do Different Calculations Yield Varying Limits for e?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
4K