- #1

chwala

Gold Member

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- 375

- Homework Statement
- See attached

- Relevant Equations
- separation of variables

My interest is only on the highlighted part, i can clearly see that they made use of chain rule i.e

by letting ##u=1+x^2## we shall have ##du=2x dx## from there the integration bit and working to solution is straightforward. I always look at such questions as being 'convenient' questions.

Now to my question, supposing we had ##x(1+x^2)^{-\frac{1}{5}} dx## in the place of ##x(1+x^2)^{-\frac{1}{2}} dx##

How would we handle this?

by letting ##u=1+x^2## we shall have ##du=2x dx## from there the integration bit and working to solution is straightforward. I always look at such questions as being 'convenient' questions.

Now to my question, supposing we had ##x(1+x^2)^{-\frac{1}{5}} dx## in the place of ##x(1+x^2)^{-\frac{1}{2}} dx##

How would we handle this?