Simple Substitution for Solving Inigral of U^-1/2

In summary, the conversation is about using substitution to solve the integral of x*dx/((1+x^2)^.5). The individual is stuck on how to get the integral into the form of u^-1/2 and is unsure of how to manipulate the numerator to equal 1. They are given the hint to use 1/u^0.5 and shown how to write a fraction as a multiplication problem. They are then asked to show their calculations for further assistance.
  • #1
Chas3down
60
0

Homework Statement


http://i.imgur.com/d0EKw.png
Initigral (x* dx/((1+x^2)^.5)

substitution
u = 1+x^2
du = 2xdx


how do get this to equal the inigral of U^-1/2

I am drawing a blank for the numerator

I know how do the problem after I get u^-1/2 .. but i need to know how to get the intigral to form of U^-1/2.. i don't know how to use substition to get to that form
 
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  • #2
what is the answer of 1/(4^2)? 0.0625
now check what is the answer for 4^(-2)? This should give you some direction...
1/(U^0.5) can then be written how?
 
  • #3
Yes, i know 1/u^1/2 = U^-1/2

But how does the numerator = 1
 
  • #4
if you have anything above the line you can make the numerator 1 and right it next to it. Like 4/6 can be written as 4*(1/6) its the same. Just show me your calcs, and I'll help you.
 

1. What is simple substitution inigral?

Simple substitution inigral is a cryptographic technique used to encrypt and decrypt messages by replacing letters or symbols with other letters or symbols according to a predetermined pattern or key.

2. How does simple substitution inigral work?

Simple substitution inigral works by using a key to determine which letters or symbols will be substituted for each other. The key typically consists of a scrambled alphabet, where each letter corresponds to a different letter or symbol in the original alphabet.

3. What is the purpose of using simple substitution inigral?

The purpose of using simple substitution inigral is to ensure the confidentiality of a message by making it unreadable to anyone who does not have the key to decrypt it. It is often used in combination with other cryptographic techniques to provide stronger security.

4. Can simple substitution inigral be broken?

Yes, simple substitution inigral can be broken through various methods such as frequency analysis, where the most commonly used letters in a language can be identified and matched to their substituted counterparts. However, using longer keys and randomizing the substitution can make it more difficult to break.

5. Are there any limitations to using simple substitution inigral?

One limitation of simple substitution inigral is that it is vulnerable to known plaintext attacks, where an attacker has access to both the encrypted and original message. It is also not suitable for encrypting large amounts of data, as it can become tedious and time-consuming to decrypt without the key.

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