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

[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

 

[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?

 

[klaus]

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

 

[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?

 

[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.

 

[Gib Z]

You can see the steps done to evaluate that integral here: http://www40.wolframalpha.com/input/pod.jsp?id=MSP10619827f2b7e0hife90000527074ag4ca4963a&s=39

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.

 

[klaus]

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.

 

[Gib Z]

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.

That's very good to hear!

When you want to check if you are right, click here:
http://www40.wolframalpha.com/input/?i=int+arctan+(+1+T/x)+dx&asynchronous=false&equal=Submit

It appears the previous link had expired =[

To see the steps on that one you have to press "Show steps" on the right of "Indefinite Integral"

 

[klaus]

thx for the updated link