Question

antidifferentiate 3x-1/x+1 please help

Answer 1

sub
u = x+1
du = dx

Answer 2

\[\int\limits \frac{3(u-1) -1}{u} du = \int\limits \frac{3u-4}{u} du = \int\limits 3 du - 4\int\limits \frac{1}{u} du\]

Answer 3

Why not simplify first?

Answer 4

Thanks that really helps.

Answer 5

\[\frac{3x - 1}{x+1} = \frac{3x + 3 - 4}{x+1} = \frac{3x + 3}{x + 1} - \frac{4}{x + 1} = 3 - \frac{4}{x + 1}\]

Answer 6

Now anti-differentiate

\[\int\left(3 - \frac{4}{x + 1}\right)dx\]

Answer 7

You can do that to avoid u-sub

Answer 8

I actually like this way better. Its easier to work out this way.

Answer 9

Which way?

Answer 10

I made it look more complicated than it really is

Answer 11

I was just showing all the steps