Question

how do you find f(x) of f'(x)=(x^4-x^2)/x^6

Answer 1

how about take the derivative?

Answer 2

i mean integral

Answer 3

Yeah how do I do that?

Answer 4

\[f'(x) = \frac{x^4 - x^2}{x^6}\]
\[\int f'(x) = \int \frac{x^4 - x^2}{x^6}\]
\[f(x) = \int \frac{x^4 - x^2}{x^6}\]
\[f(x) = \int \frac{x^4}{x^6} - \frac{x^2}{x^6}\]
getting an idea now?

Answer 5

oops minor mistake
\[f(x) = \int \frac{x^4}{x^6} - \int \frac{x^2}{x^6}\]
you might get confused

Answer 6

not really i'm kinda stuck after that part.

Answer 7

how about simplifying it first? \[\large \frac{x^m}{x^n} \implies x^{m-n}\] remember that rule?

Answer 8

\[ f(x)=\int x^{4-6}- \int x^{2-6}\\f(x)=\int x^{-2}- \int x^{-4} \]

Answer 9

haha and then after that part? sorry I just started this stuff and i'm really confused.

Answer 10

And these could be written as\[
f(x)=\int \frac{1}{x^2}- \int \frac{1}{x^4}\]

Answer 11

omg thank you i think i get it now.

Answer 12

Then simply use the fact that \[\large \int x^n dx= \frac{x^{(n+1)}}{(n+1)} + C\]

Answer 13

pellet how do I apply that?

Answer 14

Lol pellet xD

Answer 15

@lgbasallote Would explain it better than me :)

Answer 16

wtf. it said something different'

Answer 17

It's a filter

Answer 18

like @zepp said

\[f(x) = \int x^{-2} - \int x^{-4}\]
apply the rule on each one

Answer 19

And use substitution

Answer 20

\[\int x^{-2}\]
your n here is -2

so use
\[\int x^n = \frac{x^{n+1}}{n+1}\]

Answer 21

i have to go now so sorry i cannot explain further but here's an example to guide you

\[\large \int x^{-3} \implies \frac{x^{-3 + 1}}{-3} \implies \frac{x^{-2}}{-2} \implies -\frac{1}{2x^2}\]

Answer 22

^note that's not the answer that was a sample

Answer 23

why did you change the 3rd step to -2 down the bottem?

Answer 24

uhmm sorry that was supposed to be \[\frac{x^{-3 + 1}}{-3 + 1}\]
that's how it became -2 in the denominator

Answer 25

hope you got that correction
\[\int x^{-3} = \frac{x^{-3+1}}{-3+1}\]

Answer 26

okay i need to go now. good luck!

Answer 27

oh okay thank you :)

Answer 28

\[\large \begin{align}
f(x)&= \int x^{-2} - \int x^{-4} \\
f(x)&= \frac{x^{(-2+1)}}{-2}-\frac{x^{(-4+1)}}{-4}\\
f(x)&= \frac{x^{-1}}{-1} - \frac{x^{-3}}{-4}\\
f(x)&= \frac{\frac{1}{x}}{-1}-\frac{\frac{1}{x^3}}{-4}\\
f(x)&=-\frac{1}{x}-\frac{1}{-4x^3}\\
f(x)&=-\frac{1}{x}+\frac{1}{4x^3}+C\\
\end{align}\]

Answer 29

Got it? :D

Answer 30

haha yes I finally do. thank you very much guys :)

Answer 31

Good :)