How to Integrate \frac{\sqrt{x+1}}{x+3} dx with a Suitable Substitution?

  • Thread starter Ethereal
  • Start date
  • Tags
    Integration
In summary, integrating the function \frac{\sqrt{x+1}}{x+3} dx with a suitable substitution involves finding a substitution that will make the integral easier to evaluate. This can be done by letting u = x+1 and substituting it into the original function, which will result in a new integral that can be solved using basic integration techniques. By carefully choosing the substitution, the integral can be simplified and evaluated more efficiently.
  • #1
Ethereal
How does one integrate the following:
By using a suitable substitution, evaluate:
[tex]\int \frac{\sqrt{x+1}}{x+3} dx[/tex]

I tried [tex]x=tan^2 \theta, x+1=y [/tex], but the whole thing got messier. Anyone knows the correct substitution to make?
 
Physics news on Phys.org
  • #2
Here's a start: Do it in stages using the first transformation to get rid of the +1 under the radical so the integrand becomes [itex]\frac {\sqrt{x}}{x+2}[/itex] then let [itex]y = \sqrt {x}[/itex]. It should be apparent what to do next.
 
  • #3
Thanks for your help. I managed to solve it, required 2 substitutions as you said!
 
  • #4
Way to go!
 

1. What is a quick integration question?

A quick integration question is a mathematical problem in which you must find the integral of a function. Integration is the process of finding the area under a curve, and it is commonly used in physics, engineering, and other fields of science.

2. How do I solve a quick integration question?

To solve a quick integration question, you must use integration techniques such as substitution, integration by parts, or partial fractions. You must also have a good understanding of the fundamental rules of integration, such as the power rule, the constant multiple rule, and the sum rule.

3. What are some common mistakes when solving quick integration questions?

Some common mistakes when solving quick integration questions include forgetting to add the constant of integration, making algebraic errors, and not simplifying the final answer. It is important to pay attention to detail and check your work to avoid these mistakes.

4. Can I use a calculator to solve a quick integration question?

Yes, you can use a calculator to solve a quick integration question. However, it is important to note that calculators may not always give the most accurate answer and may not show the steps in the solution. It is recommended to use a calculator as a tool for checking your work, rather than relying on it completely.

5. How can I practice solving quick integration questions?

You can practice solving quick integration questions by using online resources, such as integration calculators or practice problems with step-by-step solutions. You can also find practice problems in textbooks or ask your teacher or tutor for extra practice materials.

Similar threads

  • Introductory Physics Homework Help
Replies
28
Views
262
  • Introductory Physics Homework Help
Replies
5
Views
600
  • Introductory Physics Homework Help
Replies
10
Views
863
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
813
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
857
  • Calculus
Replies
6
Views
1K
Back
Top