Integrating 1 over root x times root x plus 1 - A Guide

  • Thread starter Thread starter Khan
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the integral of the function \( \frac{1}{\sqrt{x}(\sqrt{x}+1)} \). Participants are exploring methods to simplify the integral, particularly focusing on substitutions and algebraic manipulations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of substitution, specifically \( x = u^2 \), to simplify the integral. There are mentions of encountering complications with trigonometric substitutions and the expectation of a solution involving natural logarithms.

Discussion Status

The conversation indicates that some participants are sharing their attempts and insights, with one participant noting a successful application of the substitution method. However, there remains a lack of consensus on the overall approach and solution path.

Contextual Notes

One participant expresses difficulty with the integral, suggesting that certain terms should not lead to trigonometric functions, which raises questions about the assumptions made during the substitution process.

Khan
Hey everyone, I just need a little help with this integral, I just can't get it:

integral of: (1/((x^(1/2)(x^(1/2)+1)) I know this is hard to read typed out, but said it is "Integral of 1 over the quantity root x times quantity root x plus 1. I tried doing partial fractions, but then I get stuck again.

Thanks in advance for your help!
 
Physics news on Phys.org
Did you try the substitution x = u2 to get rid of the roots?
 
I think I tried that, but that led me to a trig substition with arc tan and it's not leading my to the right answer, which I think is only with natural log.
 
Show me what you got; none of the terms involved should be quadratic, thus no arctan function.
 
Oh yea! The x=u^2 substitution did the trick actually, thanks for your help!
 

Similar threads

Power dissipated over 1 cycle of a AC source-free RLC series circuit?
  • · Replies 6 ·
Replies
6
Views
1K
Electric Field of a Toroid carrying a changing current I = kt on axis
  • · Replies 2 ·
Replies
2
Views
1K
Derivation of the Child-Langmuir law?
  • · Replies 1 ·
Replies
1
Views
4K
Solving for x in 0 = -1/8 + 3/8 x / (10^2 +x^2)^0.5
  • · Replies 10 ·
Replies
10
Views
3K
Calculating the velocity of a head-on impact between two suns
  • · Replies 6 ·
Replies
6
Views
2K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
13K
Time it Takes for a Transverse Pulse to Travel a Distance "L" Up a Cable Against Gravity?
  • · Replies 13 ·
Replies
13
Views
2K
Finding electric potential of an infinite line charge at z axis
  • · Replies 64 ·
3
Replies
64
Views
7K
Integration help on physics problem
  • · Replies 69 ·
3
Replies
69
Views
7K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
3K