Question

what is the integral of 1/x^2

Answer 1

i dont even think its possible -.-

Answer 2

-1/x+C

Answer 3

that makes sense...

Answer 4

lol, you can let u = x and du = dx and solve :) loki will show you the steps ^_^

Answer 5

You just look at it like this,\[\int\limits_{}{}\frac{1}{x^2}dx=\int\limits_{}{}x^{-2}dx=\frac{x^{-1}}{-1}+c=-x^{-1}+c=-\frac{1}{x}+c\]

Answer 6

integral x^(-2)
Just add one to the exponent and divide by the result

Answer 7

Yep.

Answer 8

what method is that?

Answer 9

Same deal. Don't be put off by the negative sign. Also, if you ever have a number that's not an integer, don't be put off by that either: add 1 and divide by the result.

Answer 10

?????????

Answer 11

Usual method...just the same you're used to when you integrate something like\[\int\limits_{}{}x dx\]

Answer 12

\[\int\limits_{}{}x^ndx=\frac{1}{n+1}x^{n+1}+c\]where n is any (real) number.

Answer 13

Here you started with n=-2.

Answer 14

Damn I overcomplicated that

Answer 15

Hehe...slightly ;)

Answer 16

slightly... dudee i used u sub, uv vdu sub, pfd, random stuff i could come up with.. i WAYYYY overcomplicated it :P

Answer 17

lol, you should calm down.

Answer 18

probably, so the integral of lnx/x^2 is lnx/x - 1/x +c

Answer 19

You can check by taking the derivative of your answer. If it's right, it should equal the integrand (the expression inside the integral). It's the Fundamental Theorem of the Calculus.

Answer 20

I get a minus outside of your lnx/x

Answer 21

you say that to everyone who askes for conformation lol and my bad, i left it back in uv vdu sub -.-

Answer 22

You should learn a method called, 'Tabular Integration by Parts'. If you understand the theory, it's good to know this method because you can punch out IBP problems with a lot less hassle.

There's a good explanation about it here: http://en.wikipedia.org/wiki/Integration_by_parts

under, ironically, 'Tabular Integration by Parts'.