Integration techniques

1. Oct 12, 2009

nameVoid

$$\int \frac{x^{1/2}}{1+x^{1/3}}$$
not sure how to start here
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 12, 2009

Count Iblis

Put x = t^6

3. Oct 12, 2009

rock.freak667

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

4. Oct 12, 2009

Staff: Mentor

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.

5. Oct 12, 2009

fghtffyrdmns

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