## anonymous 5 years ago indefinite integral of (2/cubed root of x) - 3 cubed root of x^2

1. anonymous

3/2*x^(4/3)-9/5*x^(5/3)+C using the power rule for integrals.

2. anonymous

I need some clarification on converting radical in denominator to numerator in exponential form

3. anonymous

I always get confused. so if you could list a few of them and show me I will be able to apply the power rule for intgrals thanks

4. anonymous

Ok I think I might have got it...except the 9/5 how did you get that?

5. anonymous

shouldn't it be 3/5 * x ^ (5/3)?

6. anonymous

Hold on. We're trying to integrate 2*x^(-1/3)-3*x^(2/3). So... using integral rule, 2*1/(1-1/3)*x^(2/3)-3*1/(1+2/3)*x^(5/3)= 3x^(2/3)-9/5*x^(5/3)

7. anonymous

+C. I did make a mistake initially.

8. anonymous

$2/ \sqrt[3]{x} - \sqrt[3]{x^2}$

9. anonymous

this is my question

10. anonymous

Yes. I know that. Haha.

11. anonymous

3x^(2/3)-3/5*x^(5/3)+C. Your 3 threw me off.

12. anonymous

sorry about that.. now it totally makes sense, thanks

13. anonymous

Fan me then. :D

14. anonymous

can I do one and you check and see if still understand

15. anonymous

$dt/\sqrt[3]{t}$

16. anonymous

so i get 3/2* t^2/3 +c

17. anonymous

Yup. :)

18. anonymous

i also get confused about ln|x| stuff

19. anonymous

example (2x^4 - x)/ x^3 dx = I get x^2 +x^-1 +c

20. anonymous

21. anonymous

ok I just want to know why can't I write ln|x| for x^-1

22. anonymous

You should be able to?

23. anonymous

The integral of x^-1 is ln|x|+C

24. anonymous

ok.. that's all I want to know.. it's sometimes text book shows one way and the other time it shows ln |x| without any explanation

25. anonymous

I am good on this one now thanks again

26. anonymous

It should be ln|x| because you can't take a log of a negative number.