Thread: indefinate integral

Hi I am a bit confused on how to differentiate a fraction like the problem:

integral of 2 / (3 x^1/3) dx

Im not sure where to start can you pull the 2/3 out front and just make it:

1/ x^1/3? and take ln of x^1/3?

Please help?

Originally Posted by craziebbygirl

Hi I am a bit confused on how to differentiate a fraction like the problem:

integral of 2 / (3 x^1/3) dx

Im not sure where to start can you pull the 2/3 out front and just make it:

1/ x^1/3? and take ln of x^1/3?

Please help?

the natural log only comes into play if you have 1/x, which you do not have.

note that . now integrate that using the power rule for integrals

Thanks! so would the answer be 1/2 x^4/3 + c?

also:
I have the problem: find the integral of (5x - 6) / (square root of X) dx

Can you separate it into 5x / X^1/2 - 6/x^1/2? even if I do that I still don't see how to solve it?

Originally Posted by craziebbygirl

Thanks! so would the answer be 1/2 x^4/3 + c?

no. look at the rule again. note that you have a negative 1/3 power.

Originally Posted by craziebbygirl

also:
I have the problem: find the integral of (5x - 6) / (square root of X) dx

Can you separate it into 5x / X^1/2 - 6/x^1/2? even if I do that I still don't see how to solve it?

please post one problem per thread.

Hint: