# Integration of x/(a^2+x^2)^2/3

1. May 27, 2014

### abdo799

in this video , the prof had to integrate x/(a^2+x^2)^3/2 , i know we usually do this using substitution , but in the video...he ignored the x and integrate like it was 1/(a^2+x^2)^3/2, how does that work?

Last edited: May 27, 2014
2. May 27, 2014

### micromass

Staff Emeritus

3. May 27, 2014

### abdo799

he said integration of x/(a^2+x^2)^3/2= x*(-2)/(a^2+x^2)^1/2*2x
i really dont know what he did, he differentiated the bottom part then divided by new power and multiplied by differentiation of x^2

4. May 27, 2014

### abdo799

5. May 27, 2014

### abdo799

there was a mistake with the powers in the question and i corrected it

6. May 27, 2014

### SteamKing

Staff Emeritus
Look carefully at the integrand x/(a^2+x^2)^(2/3). What is the derivative of (a^2+x^2)? Is it x times some constant perhaps? Can you rewrite the integrand as the product of two expressions, rather than the quotient?

BTW, your video requires a login to view, so we can't see it.

7. May 27, 2014

### abdo799

the power on the brakets is 3/2

#### Attached Files:

• ###### 2014-05-28 01_50_51-Another Charged Rod Problem - Lecture 2 _ U5. Another Charged Rod Problem _ .png
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8. May 27, 2014

### SteamKing

Staff Emeritus
The power on the brackets is immaterial. The principle remains.

9. May 28, 2014

### abdo799

i figured out what he did, he differentiated the bottom part...and thats it

10. May 28, 2014

### HallsofIvy

Staff Emeritus
In other words he did exactly the "$u= x^2+ a^2$" substitution, just not writing it out explicitly.