Understanding an Integral: Solving and Breaking it Down

[scottshannon]

Homework Statement

I have posted what appears to be the solution of this integral. I don't understand how the first integral was split apart in the 3rd line.

Homework Equations

The solution is included

The Attempt at a Solution

I have tried to break the integral apart but can't see how to do it...

 

[Dr. Courtney]

Looks like it might be integration by parts.

 

[scottshannon]

what would be the assignment of u and dv? Does the way that he solved this problem make sense to you?

 

[fireflies]

Did you understand the second line? The third line is Int(uv)dx= u*int(v)dx- int{u'*(int v dx)}dx

Here int=integration. latex is not working here

 

[fireflies]

It's a common formula, you must have learned it. If you don't you will find it in your textbook. It's a necessary formula to do integration

 

[DeldotB]

Good day. As Dr Courtney said it is in fact by parts. Once the integral is split into two let:

u=x
du=dx

v=-2(x^{4}+1)^{-1/2}
dv=(4x^{3})/(x^{4}+1)^{3/2}

On the first integral.

Good grief it's nearly impossible to type out latex on an iPad!

 

[Qwertywerty]

Homework Statement

I have posted what appears to be the solution of this integral. I don't understand how the first integral was split apart in the 3rd line.

Homework Equations

The solution is included

The Attempt at a Solution

I have tried to break the integral apart but can't see how to do it...

Here try this - take x² out from the denominator , and then multiply - divide by two .

See what happens .

 

[scottshannon]

Thank you for your help.

DeldotB..Thank you... I understood that it was probably integration by parts but it wasn't immediately obvious how to make the u and dv assignment.

Qwertywerty..thank you. I took out an x^2 from the denominator and multiplied by 2 on top and bottom and then was able to let u = x^2 +x^(-2) but I would not have been able to have the presence of mind to have taken out the x^2 because I couldn't have foreseen what was going to happen...but thank you.I cannot use Latex and would like to learn...is there a way to learn to use latex?

 

[Qwertywerty]

Thank you for your help.

DeldotB..Thank you... I understood that it was probably integration by parts but it wasn't immediately obvious how to make the u and dv assignment.

Qwertywerty..thank you. I took out an x^2 from the denominator and multiplied by 2 on top and bottom and then was able to let u = x^2 +x^(-2) but I would not have been able to have the presence of mind to have taken out the x^2 because I couldn't have foreseen what was going to happen...but thank you.

What you need is practice .

 

[scottshannon]

I have been trying to find problems of a nature that will allow me to do that...

 

[Qwertywerty]

I have been trying to find problems of a nature that will allow me to do that...

Why don't you ask your teacher / a mentor here ?

 

[scottshannon]

I don't have a teacher or mentor here...I don't know anyone here...

 

[Qwertywerty]

I don't have a teacher or mentor here...I don't know anyone here...

I meant a teacher at your school . You can always post at the academic guidance area if you don't want to ask your teacher .

 

[scottshannon]

Thank you but I don't go to school...I am out of school...I am just trying to learn on my own...

 

[Qwertywerty]

Thank you but I don't go to school...I am out of school...I am just trying to learn on my own...

My bad . I'm not sure how that works .

 

[scottshannon]

Qwertywerty...what was it that led you to take out an from the bottom

 

[scottshannon]

Qwertywerty...what was it that led you to take out an x² from the bottom

 

[Ray Vickson]

Thank you but I don't go to school...I am out of school...I am just trying to learn on my own...

What resources are you attempting to use? I recommend highly that you buy a copy of "Schaum's Outline of Calculus" (Google 'shaums outline series'). It starts at the elementary level and takes you through all the types of things you are asking about here; it has more than 1000 solved problems where you are taken step-by-step through the solution, and it is accompanied by instructional on-line videos. It is not expensive, ranging from about $6 to $14 (used) on Amazon.

My apologies if you are using this already and it is still not enough.

 

[Qwertywerty]

Qwertywerty...what was it that led you to take out an x2 from the bottom

Well , I could see that taking x² from the denominator would give you the derivative of the denominator - Practice

I'm sorry if I've said something obvious .

 

[LCKurtz]

I cannot use Latex and would like to learn...is there a way to learn to use latex?

Look here for LaTeX primer:
https://www.physicsforums.com/help/latexhelp/