Problem with int(arctan(B-x/tan(a))/(d-x)) dx

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In summary, the person is asking for help to calculate an integral and has provided a step by step guide.
  • #1
klaus
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hi there,

i have problems to calculate following integral:

int{ arctan [ (B - (x/tan(a)))/(d-x) ]} dx

any ideas?

thanks for the help
 
Last edited:
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  • #2
Interesting puzzle is to combine data from the title and the formatted expression to come to an actual expression to integrate! I think I've come to this:

int{ arctan [ (B - (x/tan(a)))/(d-x) ]} dx

But don't want to consider working on it untily ou can verify this is correct?
 
  • #3
sorry for the kauderwelsch (looked fine in the editor).
your assumption was correct and i have corrected it.
 
  • #4
My first guess was that it wouldn't be possible in terms of elementary functions, but Following a substitution of u= d-x you can get an integral in the form

[tex]\int \arctan \left( \frac{T+x}{x} \right) dx[/tex] where T is some constant.

That one is possible, but definitely not easy. Do you need the steps or just an answer?
 
  • #5
thx gib z,
i will try to convert it.
if its not too much trouble, i would like to see the first few steps.
 
  • #6
You can see the steps done to evaluate that integral here: http://www40.wolframalpha.com/input/pod.jsp?id=MSP10619827f2b7e0hife90000527074ag4ca4963a&s=39 [Broken]

Whilst I normally would say give it a try yourself, I'm not sure this one's worth it unless you are really good at integration or are extremely persistent.
 
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  • #7
thank you for the link.
i will give it a try myself. i am not very good at integration, but i will be very persistent.
 
  • #8
  • #9
thx for the updated link
 

What is the meaning of the equation "Problem with int(arctan(B-x/tan(a))/(d-x)) dx"?

The equation represents the integral of arctangent of the quotient of B minus x over the tangent of a, divided by the difference of d and x, with respect to x.

What is the purpose of using "Problem with int(arctan(B-x/tan(a))/(d-x)) dx" in scientific research?

This equation is commonly used in mathematical modeling and analysis of physical systems, such as in the study of heat transfer or fluid mechanics.

What are the variables represented in the equation "Problem with int(arctan(B-x/tan(a))/(d-x)) dx"?

The variables in the equation are B, a, d, and x. B and a represent constants, while d and x represent variables that can change.

Is "Problem with int(arctan(B-x/tan(a))/(d-x)) dx" a difficult equation to solve?

The level of difficulty in solving this equation depends on the specific values of the constants and variables involved. In some cases, it may be easily solved using integration techniques, while in others it may require more advanced mathematical methods.

How is "Problem with int(arctan(B-x/tan(a))/(d-x)) dx" related to real-world problems?

This equation can be used to model and solve various physical problems, such as finding the rate of change of temperature in a system or determining the velocity of a moving object. Its applications can be seen in engineering, physics, and other scientific fields.

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