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

1. Oct 30, 2009

### klaus

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: Oct 30, 2009
2. Oct 30, 2009

### mikeph

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. Oct 30, 2009

### klaus

sorry for the kauderwelsch (looked fine in the editor).
your assumption was correct and i have corrected it.

4. Oct 30, 2009

### Gib Z

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

$$\int \arctan \left( \frac{T+x}{x} \right) dx$$ where T is some constant.

That one is possible, but definitely not easy. Do you need the steps or just an answer?

5. Oct 30, 2009

### klaus

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. Oct 30, 2009

### Gib Z

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.

Last edited by a moderator: May 4, 2017
7. Oct 30, 2009