Integrating arctan(1/x) with Integration by Parts

[mpgcbball]

im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts?
thanks

 

[dextercioby]

Here's the first line

$$\int \arctan \frac{1}{x} {} dx =x\arctan \frac{1}{x}-\int x \frac{-\frac{1}{x^2}}{1+\frac{1}{x^2}} {} dx$$

 

[mpgcbball]

im not really understanding how to get that line. i don't know what to assign as u and dv. the xarctan1/x is the part that confuses me because i don't see where the x comes from

 

[trajan22]

Take it to be 1* arctan(...) then your dv will be 1.

 

[mpgcbball]

that doesn't make any sense to me, but thankyou for trying to help. i don't know what "it" is referring to that I am supposed to be taking as 1*arctan(?)

 

[mpgcbball]

ooooh i get it! thank you

 

[mpgcbball]

im still getting stuck at xarctan(1/x)-int(-x/x^2+1)

 

[dextercioby]

Can you then integrate

$$\int \frac{x}{x^2 +1} {}dx$$

?

 

[trajan22]

I haven't actually done it but if you are right up to that point then it appears that all you have to do is make a simple u substitution to solve the integral.
$$\int \frac{x}{x^2 +1} {}dx$$

 

[theperthvan]

what is the derivative of $$\ln(x^2 + 1)$$ ?