Integrating brackets

SmOgER

How do you integrate this:

?

If I do it the simple way (and the only one I know), I get:

yet the proper answer is TOTALLY different:

I don't get it... :mad:

(edited 10 years ago)

Original post by SmOgER

How do you integrate this:

?

If I do it the simple way (and the only one I know), I get:

yet the proper answer is TOTALLY different:

I don't get it... :mad:

Whoo! You are making up crazy integration rules - I promise you have never been taught to do the thing you call the "simple way".

Expand the bracket and divide each term by the denominator then integrate term by term.

dx is appearing in very odd (and wrong) places in your answer by the way.

(edited 10 years ago)

Reply 2

Phichi

11

Here take a look at this, expanding on Mr M's point. Sorry about the handwriting and pen, I just found this orange pen, now its my favorite and I must use it

Spoiler

Original post by Phichi

Here take a look at this, expanding on Mr M's point. Sorry about the handwriting and pen, I just found this orange pen, now its my favorite and I must use it

Spoiler

Do you not think all that is a trifle unnecessary even if it is a delightful shade of orange?

Reply 4

Phichi

11

Original post by Mr M

Do you not think all that is a trifle unnecessary even if it is a delightful shade of orange?

But its orange :< I guess its kind of overboard, but either way it looks cool, and in the off chance OP didn't understand, it shows the logic :s-smilie:

*Justifying himself rapidly*

(edited 10 years ago)

Reply 5

SmOgER

OP

gosh how I hate the trigonometry...

You see at first I tried expanding the brackets, but looking at the answer I couldn't understand how could integral of (2x/x^2) be -2ln|x| and how come integral of (1/x^2) is (-1/x) so I assumed it was wrong.

But now I realized that 2x/x^2 is simply = to 1/2x
and 1/x^2 is simply x^-2 and therefore adding one to power and dividing by result (-1) we get -1/x.

Actually I feel kinda dumb as it now looks so obvious :biggrin:

Thanks.

(edited 10 years ago)

Original post by SmOgER

gosh how I hate the trigonometry...)

Original post by SmOgER

But now I realized that 2x/x^2 is simply = to 1/2x

That isn't correct.

Reply 7

TenOfThem

18

Original post by SmOgER

gosh how I hate the trigonometry...

what particular trigonometry do you hate?

Reply 8

brianeverit

9

Original post by SmOgER

gosh how I hate the trigonometry...

You see at first I tried expanding the brackets, but looking at the answer I couldn't understand how could integral of (2x/x^2) be -2ln|x| and how come integral of (1/x^2) is (-1/x) so I assumed it was wrong.

But now I realized that 2x/x^2 is simply = to 1/2x
and 1/x^2 is simply x^-2 and therefore adding one to power and dividing by result (-1) we get -1/x.

Actually I feel kinda dumb as it now looks so obvious :biggrin:

Thanks.

\frac{2x}{x^2}=\frac{2}{x} \mathrm{\ NOT\ }\frac{1}{2x}

Integrating brackets

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