Question

Integrate: x(arctanx) dx

Answer 1

\[\int\limits_{}^{}x \arctan(x) dx\]
This is what I would do: make a substitution and then use integration by parts

Answer 2

parts is it

Answer 3

get
\[\frac{1}{2}x^2\arctan(x)-\frac{1}{2}\int \frac{x^2}{x^2+1}dx\] pretty much in your head, but have fun with the second integral. i leave that for myininaya

Answer 4

wow must be a hard one
i would divide first

Answer 5

get
\[\int\frac{x}{x^2+1}dx=\int 1dx-\int \frac{1}{x^2+1}dx\] then i would take a break

Answer 6

alright, so like long division?

Answer 7

how did you get the first step? the one you got from your head?

Answer 8

parts
\[\int f dg =fg-\int gdf\] with
\[f=tan^{-1}, dg = x, g =\frac{x^2}{2}, df =\frac{1}{x^2+1}\]