Question

How do I go about solving the integration of Sqrt(x) (x^2+10) all over x^4 dx?

Answer 1

deezil you are missing square root of x

Answer 2

oh sorry i sure am lol lemme fix it

Answer 3

\[(x^{1/2})(x^2+10)* x ^{-4}\]

Answer 4

u want answer??

Answer 5

Okay I've done that and integrated but it doesn't appear right

Answer 6

what'd you get?

Answer 7

-2^\[-2^(3/2) (x^3/3 +10x)/9x^3 + c\]

Answer 8

that 3/2 is an exponent

Answer 9

yeah i got you, use { } for exponents instead of ( )

Answer 10

kk thanks, how did you get that?

Answer 11

what are you talking about division and multiplication rule... he's integrating? Either i'm really out of it or I have no idea what you are talking about

Answer 12

oh sh&t i've been deriving the whole time!
so sorry lemme change it

Answer 13

I believe you're thinking derivative, this is integration haha

Answer 14

There is no quotient rule for integration. It is called Integration by parts and that would not be hard at all as you could use tabulars method

Answer 15

the top goes to 0

Answer 16

thanks outkast, I have a bad habit of not reading the entire question!

Answer 17

it's ok i was like what in the world...

Answer 18

Yeah now i see why our answers were so far off!

Well, if you ever need to derive same thing... lol

Answer 19

ok now I'm getting...

Answer 20

i believe you would tackle it the same though i can easily do by parts but i'm not sure if he's in calculus 2 or 3

Answer 21

or 1

Answer 22

2

Answer 23

\[-(2(x^2+2))/x^{5/2}\]

Answer 24

why does it become \[x^2+2\]

Answer 25

scratch that you cannot use parts since u does not go to 0 i forgot there was a sqrt

Answer 26

split x^2+10 into 2 integrals

Answer 27

or simply do it there is something they do at the end but is your answer this

\[\frac{-2}{x^{1/2}}-\frac{4}{x^{5/2}}\]

Answer 28

ahh they use the LCD which is x^2

Answer 29

I got \[-2x^{3/2}(x^2+10)/9x^3\]

Answer 30

alright so lets go through this by steps

first you want to get everything ready to integrate so times the dtop by x^-4 correct?

\[\sqrt{x}(x^2+10)(x^{-4})\]

=\[(x^{3/2}+10x^{1/2})(x^{-4}) = x^{-5/2}+10x^{-7/2}\]

Answer 31

no divide

Answer 32

well yes multiply by x^-4 my bad

Answer 33

it was divide by x^4 so you are correct

Answer 34

now using the integration rule which is add one to the exponent and divide by that number\[\int\limits_{}^{}x^{-3/2}+10x^{-7/2}=-2x^{-1/2}-4x^{-5/2}\]

Answer 35

yes that is correct i made a mistake in the above it should be \[x^{-3/2} instead of x^{-5/2}\]

Answer 36

how is it to the -3/2?

Answer 37

\[x^{5/2}*x^{-8/2} = x^{-3/2}\]

Answer 38

\[x^{-8/2}=x^{-4}\]

Answer 39

isn't it \[x^{3/2} * x^{-8/2}\]

Answer 40

anyways

what you have above is
\[\frac{-2}{x^{1/2}}-\frac{4}{x^{5/2}}\]

Answer 41

no because\[x^{1/2}*x^2=x^{1/2}*x^{4/2}\]

Answer 42

ahh

Answer 43

when dealing with exponents you add correct? so you wouldn't add
\[\frac{1}{2}+2=\frac{3}{2}\]

Answer 44

that is incorrect you'll have to find a lcd and then add

Answer 45

when dealing with the multiplication of two exponents

Answer 46

anyways you'll get the asnwer above and then you'll have to get the LCD for the two below which is x^2

\[\frac{(-2)(x^2)-4}{x^{5/2}}=\frac{-2x^2-4}{x^{5/2}}=\frac{-2(x^2+2)}{x^{5/2}}\]

Answer 47

which is your answer

Answer 48

thank you

Answer 49

no problem