Efficient Integration Techniques for Complex Functions

[nameVoid]

<br /> \int \frac{x^{1/2}}{1+x^{1/3}}<br />
not sure how to start here

 

[Count Iblis]

Put x = t^6

 

[rock.freak667]

try a trig substitution like x=atan⁶θ. Can't really say what a good value for 'a' would be so.

 

[Mark44]

I think Count Iblis's suggestion is a good one.

Also, you should get into the habit of including the differential in your integrals, like this:
\int \frac{x^{1/2}}{1+x^{1/3}}dx
If you consistently leave it out, you'll set yourself up for big problems when you integrate using trig substitutions and other techniques.

 

[fghtffyrdmns]

Like Count Iblis, I was going to suggest changing variables.