You are Here: Home

# Integration by substitution watch

1. All the other questions seemed so easy

int. between limits 5 - 1 of x/(2x-1)^(3/2) dx

It doesnt tell you what to substitute, so I opted for u^(2/3)=2x-1...

So to make the dU/dX i had to integrate implicitly... erm yeah... then it gets really weird numbers and I get the wrong answer; any help would be appreciated
2. can you post the answer please? I just don't want to post an incorrect solution and frighten you
3. 4/3
4. (Original post by Talwin)
All the other questions seemed so easy

int. between limits 5 - 1 of x/(2x-1)^(3/2) dx

It doesnt tell you what to substitute, so I opted for u^(2/3)=2x-1...

So to make the dU/dX i had to integrate implicitly... erm yeah... then it gets really weird numbers and I get the wrong answer; any help would be appreciated

Let u=2x-1

So you are left with 1/4int.sqrtu+1/4int.u^-3/2 (which requires only P1 knowledge to integrate).
5. Thankyou, but how did you get from int. (1 + u)/u^(3/2) du to 1/4int.sqrtu+1/4int.u^-3/2 ? ... have I gone wrong somewhere?
6. ∫x/(2x-1)^(3/2)dx
let u = 2x-1
so x = (u +1)/2

du/dx = 2 so dx = du/2

(1/2)∫(u+1)/u^(3/2) du/2

take out the half:

(1/4)∫(u^(-1/2) + u^(-3/2) du

giving:

(1/4)[2.u^(1/2) - 2.u^(-1/2)]

=(1/2)[(2x-1)^(1/2) - (2x-1)^(-1/2)] and this is between 1 and 5

so it equals:

(1/2)[(3 - 1/3) - (1 - 1)]

(1/2)[8/3]

= 4/3

Hope this helps.
7. thanks makes sensee...no...

OMG!! MY BROTHER JUST STROLLED INTO MY ROOM IN A DRESS AND MAKE UP!!!
8. yeah... it happened, but i will avoid going off topic

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 3, 2004
Today on TSR

### Uni league tables

Do they actually matter?

### University open days

• Staffordshire University
Everything except: Midwifery, Operating Department Practice, Paramedic Undergraduate
Sun, 21 Oct '18
• University of Exeter
Wed, 24 Oct '18