Question

how to find anti-derivative for
(x^1/3-3)/(x^2/3)
and
(e^x +3)/(e^x)

Answer 1

1/ = x^(1/3)(x ^(-2/3) - 3 x^(-2/3)
take int to get the answer
2/ =1 + 3e^(-x)
take int to get the answer

Answer 2

what is int?

Answer 3

i did everything you did but I am confused for finding the anti-derivitive

Answer 4

antiderivative is integral

Answer 5

can you go through it step by step with me

Answer 6

@zepdrix

Answer 7

i am confused because of the product rule and quotient rule

Answer 8

\[\Large\bf\sf \frac{x^{1/3}-3}{x^{2/3}}\quad=\quad \frac{x^{1/3}}{x^{2/3}}-\frac{3}{x^{2/3}}\quad=\quad x^{-1/3}-3x^{-2/3}\]Simplify before looking for the anti-derivative.
Understand those steps?

Answer 9

We don't have a nice product rule or quotient rule for anti-differentiation.
So simplifying first is necessary.

Answer 10

yes i already did that but i am confused for what to do next

Answer 11

Next we apply the `Power Rule for Anti-Differentation`:
The anti-derivative of \(\Large\bf\sf x^n\) will be \(\Large\bf\sf \dfrac{1}{n+1}x^{n+1}\)

2 steps:
~Increase the power by 1,
~Divide by the new power.

This looks familiar yes?

Answer 12

Our exponents are fractions, so it will be a little bit messier.

Answer 13

yes i understand that

Answer 14

I am having trouble understanding your abbreviations though

Answer 15

abbreviations?
You shouldn't see abbreviations.
Is the math code not loading correctly?

Answer 16

its not loading

Answer 17

\(\Large\bf\sf x^n\) will be \(\Large\bf\sf \dfrac{1}{n+1}x^{n+1}\)

Answer 18

Ugh, the LaTeX plugin has been acting weird today :(
Are you using Internet explorer?

Answer 19

google chrome

Answer 20

i could try safari?

Answer 21

It should work fine on Chrome.. that really stinks.

Answer 22

The alternative is the drawing tool, which I know doesn't work.. Hmm :p

Answer 23

i tried inserting it on wolfram

Answer 24

antiderivative of x^n is (1/(n+1)) * x^(n+1)

Answer 25

I can do it like that I guess.. it's just a lot uglier XD lol

Answer 26

lol its fine. Thanks for your help. I really appreciate it.

Answer 27

So for the first term,
The -1/3 .... adding 1 will change it to 2/3.
Then we divide by that new exponent, (which is the same as multiplying by the reciprocal, yes?

Answer 28

We would divide by 2/3, or multiply by 3/2

Answer 29

okay i follow you there

Answer 30

so what would it look like expressed out? 2/3x^4/3

Answer 31

So antiderivative of the first term:

(3/2)x^(2/3)

Answer 32

okay so we are going to find all antiderivities in 1 step? Should i use the anti-derivitive blank integral sign?

Answer 33

woops, i had simplified things down earlier..
maybe the code didn't show up though.

We're antidifferenting these two terms:
x^(-1/3)-3x^(-2/3)

Answer 34

blank integral sign? :o you mean the curly S thing?

Answer 35

yeah sorry

Answer 36

and there is no x^-1/3??

Answer 37

can you just do it and take a snap shot and upload it?

Answer 38

Mmm lemme see if I can pull that off.
One sec lemme test the drawing tool

Answer 39

M:mm darn no drawing tool.. one sec

Answer 40

okay thanks

Answer 41

Okay let's see if this works or not.

Answer 42

it works. Thanks!!!

Answer 43

For the next problem, is the 3 supposed to be in the exponent position or no?

e^(x-3) or e^x - 3

Answer 44

Err it's +3 but hopefully you know what I'm asking :x

Answer 45

wolfram alpha and copy and paste it.

Answer 46

http://www.wolframalpha.com/input/?i=%28e%5Ex+%2B3%29%2F%28e%5Ex%29

Answer 47

The next one is very similar.

Answer 48

If you get confused on the anti-derivative of e^(-x),
hmm I'm not really sure if I can explain that in a way that you'll understand.
I wonder if you've learned enough to be able to do that.

Have you learned U-substitution for integration yet?

Answer 49

no.

Answer 50

I can tell my teacher it was undoable and he will understand

Answer 51

thanks for all of your help

Answer 52

np c: