Linear Rationalizing Substitution problem for Integration

So I'm working with the following problem - http://i1057.photobucket.com/albums/...ps245f8e94.png

After setting u = 2x + 1, and (1/2)du = dx, and x = ((u-1)/2) I end up with

(1/2)integral{((u-1)\2)^{3 }(u)^{(1/3)}du}

After doing that I get lost. What would be the next step? Do I need to make another substitution?

(I can't do (1/4)((u-1)/2)^{4} can I?...)

Re: Linear Rationalizing Substitution problem for Integration

Quote:

Originally Posted by

**Shadow236** So I'm working with the following problem -

http://i1057.photobucket.com/albums/...ps245f8e94.png
After setting u = 2x + 1, and (1/2)du = dx, and x = ((u-1)/2) I end up with

(1/2)integral{((u-1)\2)

^{3 }(u)

^{(1/3)}du}

After doing that I get lost. What would be the next step? Do I need to make another substitution?

(I can't do (1/4)((u-1)/2)

^{4} can I?...)

Hint :

$\displaystyle (A-B)^3=A^3-3A^2B+3AB^2-B^3$

Re: Linear Rationalizing Substitution problem for Integration

The thing is, I have ((u-1)/2)^{3}. So I can't re-write is as (u-1)^{3} x (1/2)^{3}... can I?

Re: Linear Rationalizing Substitution problem for Integration

I just have one question can we solve these kind problems by asking questions like these. Why don't you contact some expert who can work on these kind problems, who have already worked on these kind of problems. I suggest you If you have these many difficulties in solving the mathematics problems you can contact https://artifextutors.com and just send you question to them on questions@artifextutors.com I am sure that they will be able to help you. Artifex Tutors Homework help, Assignment help, Online Tutor, Physics, Chemistry, Math, Statistics, Finance, Economics, Accounting

Regards

Jean

Re: Linear Rationalizing Substitution problem for Integration

I think that the MHF community is willing to help me, and has helped me in the past. In all honesty, directing me to some other site that in no way relates to my problem is not helping me.

Re: Linear Rationalizing Substitution problem for Integration

Every person does have their own view I am not saying you are wrong. I just gave you an alternate in case you get stuck in the future there are some more people who can help you.

Regards

Jean

Re: Linear Rationalizing Substitution problem for Integration

Well, thank you, I guess.

Anyway, how do I integrate ((u-1)/2)^{3}?

Re: Linear Rationalizing Substitution problem for Integration

Shadow

expand the expression( (u-1)/2)^3 then multiply by u^1/3 and integrate the polynomial you will obtain.

It is a little bit messy but if you are lucky and you will work slowly you will not do mistakes.

Give it a try.

MINOAS

Re: Linear Rationalizing Substitution problem for Integration

It turns out that that was one of the methods I tried, but I just got lost in the arithmetic. Thanks a lot!