integrate (5x+2)dx/(x-2) from 0 to 1


by erjkism
Tags: 2dx or x2, integrate
erjkism
erjkism is offline
#1
Dec8-07, 07:14 PM
P: 54
1. The problem statement, all variables and given/known data

[tex]\int\frac{(5x+2)dx}{x-2}[/tex] from 0 to 1


2. Relevant equations

3. The attempt at a solution

ive tried splitting it up into (5x)/(x-2) + (2)/x-2), but i couldnt go any farter. Ived also tried using lots of U subsitutions, but i cant figure out what do next. Is there some trick that i am not seeing?
Phys.Org News Partner Science news on Phys.org
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
Dick
Dick is offline
#2
Dec8-07, 07:15 PM
Sci Advisor
HW Helper
Thanks
P: 25,178
Yep, the obvious one. u=x-2. dx=du. x=2+u.
robphy
robphy is offline
#3
Dec8-07, 07:22 PM
Sci Advisor
HW Helper
PF Gold
robphy's Avatar
P: 4,108
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.

rocomath
rocomath is offline
#4
Dec8-07, 07:28 PM
rocomath's Avatar
P: 1,757

integrate (5x+2)dx/(x-2) from 0 to 1


Quote Quote by robphy View Post
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.
Woah, woulda never thought of that. Nice, I want your vision :-]
Dick
Dick is offline
#5
Dec8-07, 07:38 PM
Sci Advisor
HW Helper
Thanks
P: 25,178
Quote Quote by robphy View Post
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.
You'll still want u=x-2 to do the 12/(x-2) part.
Mystic998
Mystic998 is offline
#6
Dec8-07, 08:00 PM
P: 206
Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.
robphy
robphy is offline
#7
Dec8-07, 08:08 PM
Sci Advisor
HW Helper
PF Gold
robphy's Avatar
P: 4,108
Quote Quote by Dick View Post
You'll still want u=x-2 to do the 12/(x-2) part.
True... and now the substitution is really obvious.


Register to reply

Related Discussions
What is the best way to integrate this?? Calculus 22
How do you integrate this?? General Math 6
Integrate ln(4+y^2)dy? Calculus 8
How do I integrate this? Calculus & Beyond Homework 4
how to integrate??? Calculus & Beyond Homework 5