Question

evaluate the integral: 2x+5/x+1 dx

Answer 1

Let's see...
\[\huge \int \frac{2x+5}{x+1}dx\]

Answer 2

What approaches have you tried?

Answer 3

this will help: split it up into two integrals, 2x/x+1 and 5/x+1. use u substitution and manipulate u.

Answer 4

No, @lilminiwin you do split the two integrals, but there is a much better way, methinks...
I'll wait for @Juan07 's approach.

Answer 5

Okay.... I'm alone~
No matter....
You split it like this...
\[\Large \int \frac{2x+5}{x+1}dx = \int \frac{2x+2+3}{x+1}dx = \int \left[\frac{2x+2}{x+1}+\frac3{x+1}\right]dx\] and that's much easier.

Answer 6

I'll concede that that was slightly easier.

Answer 7

Still confused, @Juan07 ?
How about I do one more small step...
\[\Large = \int \left[\frac{2(x+1)}{x+1}+\frac3{x+1}\right]dx\]

Answer 8

ok thanks for your help

Answer 9

:D

Answer 10

No problem.