Question

how to integrate x^2/(1+x^3)

Answer 1

i will show you a trick to solve this problem

Answer 2

Thanks so much

Answer 3

as you can see the numerator holds the derivative of the denomirator

Answer 4

the answer would be

Answer 5

\[\frac{ 1 }{ 3 }\ln(1+x^{3})\]

Answer 6

how did this happen?

Answer 7

The problem is what we're the steps?

Answer 8

yes i will show you the steps

Answer 9

but i want you to visualize what is going on

Answer 10

before i show u the steps

Answer 11

Thanks I've been trying or two hours

Answer 12

please bear in mind a fact in calculus when you see the derivative at the numerator of the denominator then it is a natural log

Answer 13

please let me know if you don't understand what i mean

Answer 14

step one: let u = \[(1+x^{3})\]

Answer 15

Yes I understand

Answer 16

step two: d.w.r.x -> \[\frac{ du }{ dx }=3x ^{2}\]

Answer 17

this means that : \[dx = \frac{ du }{ 3x ^{2} }\]

Answer 18

Ok so ffar

Answer 19

step three: look at the main function you are trying to integrate which is : \[\int\limits_{}\frac{ x^2dx }{ 1+x^3 }\]

Answer 20

now put that in terms of the u

Answer 21

\[\int\limits\limits_{}\frac{ x^2du }{ 3x^2u }\]

Answer 22

now tell me do you see what is going on?

Answer 23

\[\frac{1}{3}\int\limits\limits\limits_{}\frac{ du }{ u }\]

Answer 24

Yes so far

Answer 25

\[\frac{1}{3}\ln (u) + c\]

Answer 26

now try yourself to put this last equation in terms of x

Answer 27

Yes I see it :)

Answer 28

recall \[\frac{1}{3}\ln (1+x^3) + c\]

Answer 29

Sorry couldn't type it in right

Answer 30

so now you should be able to work out by head

Answer 31

its ok

Answer 32

i gave the answer

Answer 33

Yes I was so confused on how the 1/3 was coming in front of the ln

Answer 34

I can't thank you enough

Answer 35

its ok if you have another question i can answer it hopefully

Answer 36

you can give me a medal hehehe

Answer 37

For now that's it , but are you usually online? I might have a question later

Answer 38

not really not always

Answer 39

Of course you deserve a hundred medals..just how do I give u one

Answer 40

i only was here since yesterday but there are others who can help as well

Answer 41

i don't know hehehe

Answer 42

Il find out..ur getting the medal

Answer 43

thanx that is kind of you

Answer 44

you are a clever girl you pick up quick the answer

Answer 45

It was part of my Differential equation hw..I was stuck on the integration

Answer 46

what year are you?

Answer 47

http://www.mathway.com/math_image.aspx?p=SMB02FSMB03xSMB02ESMB032SMB02eSMB03SMB10(x+1)(xSMB02ESMB032SMB02eSMB03-x+1)SMB02fSMB03?p=125?p=42

Answer 48

Junior but haven't taken calc in over 5 years!

Answer 49

oh ok

Answer 50

man too many questions on this forum

Answer 51

right

Answer 52

You? Math major

Answer 53

no i am a communication engineer

Answer 54

Cool well best of luck and thanks again :)

Answer 55

you too all the best i will see who can i help here