Question

Find an anti-derivative for each of the following -2/x^3

Answer 1

yes

Answer 2

\[\Large \int\limits\limits_{}^{}\frac{-2}{x^3} dx\] sorry, I had to fix my notation

Answer 3

Well first you gotta factor out the -2 the integrand

Answer 4

Extricate it out?

Answer 5

Factor, but if you want to say that lol, it must go on the outside though

Answer 6

"Extricate it out" ?
Dude, calm down.

Answer 7

\[\Large -2\int\limits_{}^{}\frac{1}{x^3} dx\]

Answer 8

ok*

Answer 9

why you put 1 ?

Answer 10

Because I factored the -2 out, since I took it out, you have to leave a 1, its like you multiply it in there -2*1=-2 its the same thing.

Answer 11

ok

Answer 12

anyways you have to change the fraction to an x with a negative exponent to use the Power Rule for integration

Answer 13

what's the Power Rule for integration ?

Answer 14

Do you know the power rule for integration? \[\Huge \int\limits_{}^{}x^{n}~dx=\frac{x^{n+1}}{n+1}\]

Answer 15

Because the first time I am studying integration

Answer 16

ok

Answer 17

But we have no shrine and the extension .. how we ride it rule?

Answer 18

Alright now remember we have
\[\Large -2\int\limits\limits_{}^{}\frac{1}{x^3} dx \] We have to change the \[\Large \frac{1}{x^3} ~to~x^{-3}\]
\[\Large -2\int\limits\limits\limits_{}^{}{x^{-3}} dx\]
\[\Large -2(\frac{x^{-3+1}}{-3+1}) +C\]

Answer 19

aha thanks a lot

Answer 20

Don't forget you gotta fix it up \[\Large -2\frac{x^{-2}}{-2} +C\]
\[\Large x^{-2}+C \]
\[\Large \frac{1}{x^2}+C\]
Do you know why you have to put a C

Answer 21

yes

Answer 22

Alright, good luck, it only gets harder!!!