Question

how to integrate \[\int \frac{2+v}{1+v^2}\]

Answer 1

Separate into 2 fractions:
\[\frac{2}{1+v^2}+\frac{v}{1+v^2}\]
then integrate separately.

Answer 2

seperate it into 2 integ question first is intg (2/(1+v2))
and the other is 1/2 intg(2v/(1+v2))
and thus the ans is 2tan-1 v +1/2 ln|1+v2| + c

Answer 3

@blockcolder how do you integrate 2/(1+v)^2

Answer 4

Don't you mean 2/(1+v^2)?

Answer 5

yeah

Answer 6

Here's a rule for safe-keeping:
\[\int \frac{1}{1+x^2} dx=\tan^{-1}x+C\]

Answer 7

oh..yeah of course *facepalm*