Help for this infinite integral question ?

In summary, an infinite integral is a mathematical operation used to find the area under a curve that extends to infinity. It is important to find solutions for these integrals because they have many practical applications in various fields. To solve an infinite integral, it is best to break it down into smaller parts and use techniques such as substitution, integration by parts, or partial fractions. However, not all infinite integrals have an analytic solution, and some may require numerical methods or approximations. To solve them more efficiently, it is helpful to look for symmetries or patterns in the integrand and understand the limits of integration. Experience with different integration techniques can also improve efficiency.
  • #1
erogol
14
0
[tex]\int (((ax^2)/(x^3)+5) + 2 / x^3) dx[/tex] (one to infinite integral) find the all possible values of a?
 
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  • #2
I can't imagine your parentheses are correct...
 
  • #3
Is this supposed to be:


[tex]\int_{1}^{\infty}\left({\frac{ax^2}{x^3+5}+\frac{2}{x^3}\right)dx[/tex]

>??
 

FAQ: Help for this infinite integral question ?

What is an infinite integral?

An infinite integral is a type of mathematical operation that involves finding the area under a curve that extends to infinity. This means that the limits of integration are from negative infinity to positive infinity.

Why is it important to find solutions for infinite integrals?

Infinite integrals have many applications in physics, engineering, and other sciences. They can be used to calculate the work done by a force, the volume of an irregularly shaped object, or the amount of heat dissipated in a system, among other things.

How do you approach solving an infinite integral?

Solving an infinite integral usually involves breaking it down into smaller, more manageable parts. This can be done by using techniques such as substitution, integration by parts, or partial fractions. In some cases, it may also require the use of advanced mathematical concepts such as series or improper integrals.

Can all infinite integrals be solved analytically?

No, not all infinite integrals have an analytic solution. In some cases, the integral may not converge, meaning that it does not have a finite solution. In these cases, numerical methods or approximations may be used to find an approximate solution.

Are there any tips for solving infinite integrals more efficiently?

One useful tip for solving infinite integrals is to look for symmetries or patterns in the integrand. These can help simplify the integral and make it easier to solve. It is also important to pay attention to the limits of integration and understand how they affect the solution. Practice and familiarity with different integration techniques can also help improve efficiency.

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