# Integration by parts?

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

## Answers and Replies

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dextercioby
Homework Helper
Here's the first line

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

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

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

that doesnt make any sense to me, but thankyou for trying to help. i dont know what "it" is referring to that im supposed to be taking as 1*arctan(???)

ooooh i get it!! thank you

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

dextercioby
Homework Helper
Can you then integrate

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

?

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

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