Question

integral 9+6x/1+x^2 *dx evaluate the integral

Answer 1

interesting..

Answer 2

\[\int{9+6x\over1+x^2}dx=3\int{3+2x\over1+x^2}dx=3\int{3\over1+x^2}+
{2x\over1+x^2}dx\]that should give you a few ideas

Answer 3

you can also do \[\int \frac{9+6x}{1+x^2}dx\implies \int \frac{9}{1+x^2}dx + \int \frac{6x}{1+x^2}dx\]
same thing really

Answer 4

I make u=1+x^2

Answer 5

right

Answer 6

go on..

Answer 7

du=2x but i don"t really know what to do with the top

Answer 8

look at both lgb's way and mine
try to see how they are the same, and how you can reconcile your problem by comparing the two

Answer 9

hint: you can only use u-sub in the second integral. the first integral is trig sub