How can I determine if a given integral is solvable?

In summary, there are several steps to take when trying to determine if an integral is solvable or not. First, try conventional methods such as partial integration, substitutions, partial fraction decompositions, and the residue theorem. If these methods do not work, then search for the integral in "Gradsteyn & Rythzik". If it is not found there, it means that the primitive or antiderivative exists, but cannot be expressed through elementary functions. Another resource that may be helpful is the Wolfram Integrator, however it may not work for more complicated integrals. An example of this is the Laplace Transform of arctangent, where the result may depend on the input given.
  • #1
bomba923
763
0
Ok...now how do I know if a certain integral is solv/integrat-able or not?
Just by looking at the inside function, how can I tell if the integral can be solved or not??
 
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  • #2
How about these steps:

1.Try conventional methods:part integration,substitutions,partial fraction decompositions,residues theorem.

2.If it doesn't work,then search for it in "Gradsteyn & Rythzik".

3.If it's not there,the primitive/anitderivative exists,but it's not expressible through elementary functions.

Daniel.
 
  • #3
The Wolfram Integrator can also be helpful as a quick reference technique.
 
  • #4
Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything... :grumpy:


Daniel.
 
  • #5
dextercioby said:
Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything... :grumpy:


Daniel.
Really? Can you give me an example please.
 
  • #6
I tried an integral that comes up in the Laplace Transform of arctangent

[tex] \int_{0}^{+\infty} e^{-sx}\arctan x dx [/tex]

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.
 
  • #7
dextercioby said:
I tried an integral that comes up in the Laplace Transform of arctangent

[tex] \int_{0}^{+\infty} e^{-sx}\arctan x dx [/tex]

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.

Works fine for me when I enter:

Code: 
Exp[-s x] ArcTan[x]
 
  • #8
Thenx,Zurtex,there's no wonder i couldn't do it... :tongue2: I misstyped something... :grumpy:
I like the result,though... :tongue2:

Daniel.
 
  • #9
dextercioby said:
Thenx,Zurtex,there's no wonder i couldn't do it... :tongue2: I misstyped something... :grumpy:
I like the result,though... :tongue2:

Daniel.
Yeah I can't help thinking Wolfram are trying to introduce their own brand of maths :wink:
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to calculate the total value of a function or the displacement of an object over a given interval.

2. What is the difference between a definite and indefinite integral?

A definite integral has specific limits of integration, meaning it calculates the area under the curve between two given points. An indefinite integral does not have limits of integration and instead represents the general antiderivative of a function.

3. How do you solve an integral?

To solve an integral, you can use various integration techniques such as substitution, integration by parts, or partial fractions. The method used depends on the form of the integrand and may require multiple steps to solve.

4. What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that integration and differentiation are inverse operations. In other words, the derivative of an integral is equal to the original function, and the integral of a derivative is equal to the original function plus a constant.

5. How are integrals used in real-world applications?

Integrals have many real-world applications, such as calculating the area under a velocity-time graph to determine distance traveled, finding the volume of a solid, and determining the work done by a force. They are also used in fields such as physics, economics, and engineering to model and solve various problems.

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