Int[6/(x^2+3)^2] Solution Help

  • Thread starter badtwistoffate
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In summary, the conversation discusses different methods for solving a given integral, specifically using a trigonometric substitution. The speaker shares their initial method of setting x = 3tan(u) and using dx = 3sec(u)^2 du, but realizes that using x = √3tan(θ) and dx = √3sec^2(θ) dθ would have been a simpler approach. However, the expert summarizer notes that both methods can work and it ultimately depends on the individual's preference.
  • #1
badtwistoffate
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in int[6/(x^2+3)^2] i use 3tanU=x, dx=3sec(u)^2 du
using that i get to ... int[1+cos2u]= u + sin2u/2 = u +sin u cos u... but subing back in with trig doesn't give me the right answer... any help with this method?
 
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  • #2
[tex]I = \int {\frac{6}{{\left( {x^2 + 3} \right)^2 }}dx} [/tex]

Instead of setting x = 3tan(u) try...

[tex]
x = \sqrt 3 \tan \theta \Rightarrow dx = \sqrt 3 \sec ^2 \theta d\theta
[/tex]
 
  • #3
darn it, after looking at my work i was afraid someone would say that... as i didnt relize that would be better until i finished it and noticed it was coming out right... does that mean you can't do it my way:-/
 
  • #4
There's really no reason why it can't be done your way. It's just that some substitutions will require you to evaluate much more complicated integrals than if you were to use a substitution which obviously simplifies the integrand.
 

1. What is the given expression "Int[6/(x^2+3)^2]"?

The given expression is an indefinite integral, which represents the antiderivative or the reverse process of differentiation. It is a mathematical operation that involves finding a function whose derivative is the given expression.

2. What does the "Int" notation in the given expression stand for?

The "Int" notation stands for "integral," which is a mathematical concept used to calculate the area under a curve. It is represented by the symbol ∫ and is the inverse operation of differentiation.

3. How do I solve the given expression "Int[6/(x^2+3)^2]"?

To solve the given expression, you can use techniques such as substitution, integration by parts, or partial fractions. These techniques involve manipulating the given expression to make it easier to integrate and then using the fundamental theorem of calculus to find the solution.

4. Why is there a "dx" at the end of the given expression "Int[6/(x^2+3)^2]"?

The "dx" at the end of the given expression represents the variable of integration. It indicates that the integration is being performed with respect to the variable "x." This notation is important as it tells us which variable we are integrating with respect to.

5. Can I use a calculator to solve the given expression "Int[6/(x^2+3)^2]"?

No, you cannot use a calculator to solve the given expression. Integration is a process that requires understanding and applying mathematical concepts and techniques. While calculators may provide numerical solutions, they cannot show the steps involved in solving the integral, which is essential for understanding the concept.

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