Solve Impossible Integral: Integration by Parts?

In summary, the conversation suggests using a substitution strategy to solve the given integral, with the suggested substitution being u = arctan y. The integral is \int_{-1}^{1/\sqrt{3}}\frac{\exp(\arctan y)}{(1+y^2)}dy. The individual can choose to evaluate during the substitution or substitute back in before evaluating.
  • #1
frasifrasi
276
0
---> how do I solve this integral?

integral from -1 to 1/(sqrt(3)) of e^(arctan y) over (1+y^2)...

Am I supposed to use integration by parts or what?
 
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  • #2
As a general rule, a good strategy to try is a substitution of the form u = ugliest subpiece. In this case, u = arctan y.
 
  • #3
i definitely cannot make out what your integral is

you should really learn latek, lol. i learned latek around my 30th posting :p
 
  • #4
The integral is this: [tex]\int_{-1}^{1/\sqrt{3}}\frac{\exp(\arctan y)}{(1+y^2)}dy[/tex]

frasifrasi; click on the image to see the latex code.
 
  • #5
so, a simple u sub will work? then I would have to sub back in before evaluating, correct?
 
  • #6
correct! or you could evaluate during your substitution which changes your intervals, but it's all up to you.
 

1. How do you determine when to use integration by parts?

Integration by parts is typically used when the integrand is a product of two functions, one of which is easier to integrate than the other. In general, it is used when the integrand cannot be easily simplified or evaluated using other techniques such as substitution or partial fractions.

2. What is the general formula for integration by parts?

The general formula for integration by parts is ∫u dv = uv - ∫v du, where u and v are functions of x and dv is the derivative of v with respect to x. This formula can be remembered using the acronym "LIATE" (Logarithmic, Inverse Trigonometric, Algebraic, Trigonometric, Exponential), which helps determine which function should be chosen as u and which as dv.

3. Can integration by parts be used to solve all integrals?

No, integration by parts has its limitations and cannot be used to solve all integrals. Sometimes, it may not lead to a solution or may result in a more complicated integral. Other techniques such as substitution, partial fractions, or using trigonometric identities may be more effective in solving certain integrals.

4. How many times can integration by parts be applied?

Integration by parts can be applied multiple times in succession, with each application resulting in a simpler integral. However, it is important to choose u and dv carefully each time to avoid getting stuck in a loop or creating a more complicated integral.

5. What are some common mistakes to avoid when using integration by parts?

Some common mistakes to avoid when using integration by parts include choosing u and dv incorrectly, not simplifying the integral after each application, and forgetting to add the constant of integration. It is also important to check for mistakes in the algebraic steps, as well as to double-check the final answer using differentiation.

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