Integrate

[goku900]

I need help integrating the following;

(x^4)/(1+x^10)

I originally used a u-sub and then arctan definition to solve for it but my professor does not want it done that way. Any suggestions?

 

[Deleted member 4993]

I need help integrating the following;

(x^4)/(1+x^10)

I originally used a u-sub and then arctan definition to solve for it but my professor does not want it done that way. Any suggestions?

The most efficient way would be to follow the route that you had followed (u =x⁵)

Another way would be to use;

1 + x¹⁰ = (1 + i x⁵)(1 - ix⁵) and then use partial fraction.

 

[daon2]

I need help integrating the following;

(x^4)/(1+x^10)

I originally used a u-sub and then arctan definition to solve for it but my professor does not want it done that way. Any suggestions?

You have the right idea. If the answer has an arctan in it, your professor cannot change that. Is there a particular section this problem was assigned from that might suggest the use of a specific method?

 

[goku900]

The most efficient way would be to follow the route that you had followed (u =x⁵)

Another way would be to use;

1 + x¹⁰ = (1 + i x⁵)(1 - ix⁵) and then use partial fraction.

I'm not comfortable nor very familiar with that notation.

 

[HallsofIvy]

What notation? The use of "i"? If you are taking Calculus, you should be at least aware of imaginary numbers.