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

  • Thread starter worstcalcbook
  • Start date
  • Tags
    Integrate
In summary, the individual encountered a difficult integration problem and turned to Wolfram Alpha for help. However, the solution provided did not explain how to substitute back s = arctan (u/2) and the individual found it frustrating and unhelpful. They also mention a substitution that is similar (u = tan (x/2)), but it was not covered in their textbook. They later solved the problem on their own.
  • #1
worstcalcbook
2
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
  • #2
Nevermind, solved it. Wolfram Alpha is useless most of the time.
 

1. How do I approach solving this integral?

To solve this integral, you can use the substitution method. Let u = x^2-2x+5, then du = (2x-2)dx. This will help simplify the integral and make it easier to solve.

2. What is the domain of this function?

The domain of this function is all real numbers except for x = 1 and x = 2. This is because the denominator becomes 0 at these points, making the function undefined.

3. Can this integral be solved using partial fractions?

Yes, this integral can be solved using partial fractions. After using the substitution method, you will have a quadratic function in the denominator. You can then use partial fractions to break it down into simpler fractions that are easier to integrate.

4. Is there a specific method I should use to solve this integral?

There are multiple methods that can be used to solve this integral, including substitution, partial fractions, and trigonometric substitution. It is important to choose the method that you feel most comfortable with and that is suitable for the given function.

5. What is the final answer to this integral?

The final answer will depend on the limits of integration, if any. After solving the integral, you will be left with a constant or a variable that represents the integration constant. The final answer will include this constant, unless the limits of integration are provided.

Similar threads

I Troubleshooting a difficult integral
    • Calculus
Replies
6
Views
1K
B Integration by parts of inverse sine, a solved exercise, some doubts...
    • Calculus
Replies
4
Views
904
A Integration of the Maxwell Speed Distribution
    • Calculus
Replies
12
Views
1K
I Substitution in a definite integral
    • Calculus
Replies
6
Views
1K
MHB Integrate 3/(x(2-sqrt(x))) - No Partial Fractions
    • Calculus
Replies
5
Views
1K
I How Do You Integrate Expressions Like These?
    • Calculus
Replies
6
Views
1K
I Integration of √(1-x^2) with x=sinθ: Check Correctness and Simplification
    • Calculus
Replies
12
Views
2K
I How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?
    • Calculus
Replies
8
Views
1K
I Negative area above x-axis from integrating x^2?
    • Calculus
Replies
4
Views
1K
I Gaussian integral by differentiating under the integral sign
    • Calculus
Replies
19
Views
3K

Hot Threads

Recent Insights

Back
Top