Mastering Indefinite Integrals: Tips and Tricks for Evaluating Tricky Functions

Click For Summary

Discussion Overview

The discussion revolves around evaluating the integral \(\int\frac{dx}{\sqrt{1-2x-x^2}}\) using inverse trigonometric functions. Participants explore techniques for solving this integral, including completing the square and the role of practice in mastering such problems.

Discussion Character

  • Technical explanation, Homework-related, Exploratory

Main Points Raised

  • One participant asks how to evaluate the integral using inverse trig functions.
  • Another suggests completing the square of the quadratic expression in the integrand.
  • A participant expresses difficulty with the problem and wishes for greater creativity in finding solutions.
  • Further advice includes factoring out the negative before completing the square if it is not remembered.
  • One participant reports successfully finding the answer after receiving hints from others and questions whether solving such problems becomes easier with practice.
  • Another emphasizes the importance of reading and practicing various methods to improve skills.
  • A later reply stresses that experience with integrals is crucial and encourages doing many problems to learn the necessary techniques.

Areas of Agreement / Disagreement

Participants generally agree on the importance of practice and experience in mastering integral evaluation techniques, but there is no consensus on specific methods or the ease of finding solutions.

Contextual Notes

Some participants mention specific techniques like completing the square, but there are no detailed steps provided, and the discussion does not resolve the complexity of the integral itself.

Who May Find This Useful

Students and learners interested in improving their skills in evaluating indefinite integrals, particularly those involving inverse trigonometric functions.

uman
Messages
348
Reaction score
1
How can I evaluate \int\frac{dx}{\sqrt{1-2x-x^2}} using inverse trig functions? Thanks.
 
Physics news on Phys.org
complete the square of the quadratic.
 
Oh... thanks.

Dang these are so hard... I wish I had the creativity to see the solution immediately like that...
 
ax^2+bx+c, a=1, factor out the negative before you complete the square if you didn't remember.
 
Thanks. I got the right answer after rock.freak667's hint. I just wish I were able to solve these more easily, without hints from this forum and elsewhere... does it just take lots of practice, or what?
 
Read read read! And do the practice problems :-]

Go here to see a variety of diff. methods.

http://www.mathlinks.ro/weblog_entry.php?p=992552#992552
http://www.mathlinks.ro/weblog_entry.php?p=992575#992575
http://www.mathlinks.ro/weblog_entry.php?p=992703#992703
 
Last edited by a moderator:
When it comes to integrals, its experience that really counts. Do as many integrals as you can, you'll soon learn the tricks of the trade.
 

Similar threads

Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
MHB Differentiation under integral sign
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Improper Integrals: Definite & Indefinite | Bounds -1 to 1
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why is the integral of ##\arcsin(\sin(x))## so divisive?
  • · Replies 3 ·
Replies
3
Views
3K
High School Arc Length for Hyperbolic Sin
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Is there a way to find the indefinite integral of e^(-x^2) or e^(x^2)?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Limit Definition of Indefinite Integrals?
  • · Replies 6 ·
Replies
6
Views
4K