Question

This integral is giving me trouble (x^2 +2)/(x^2 +1) dx. Anyone want to be a hero and help me out?

Answer 1

i think you have to divide first, then use partial fractions
maybe i am wrong

Answer 2

= ( x² + 1 ) / ( x² + 1 ) + 1/ ( x² + 1 )
Then take integral

Answer 3

oh i am wrong
but you do need to divide first, and there is an easy trick to doing it
\[\frac{x^2+2}{x^2+1}=\frac{x^2+1+1}{x^2+1}=1+\frac{1}{x^2+1}\]

Answer 4

what @Chlorophyll said

Answer 5

btw you are supposed to recognize the second integral, not compute anything

Answer 6

Wow, thank you so much guys. I was doing all kinds of crazy trig triangle subs, integration by parts, and u subs trying to figure this out. Glad to see it's so simple. Cheers!