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Integrating brackets watch

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    How do you integrate this: Name:  1.png
Views: 240
Size:  851 Bytes ?

    If I do it the simple way (and the only one I know), I get:
    Name:  2.png
Views: 244
Size:  3.2 KB

    yet the proper answer is TOTALLY different:

    Name:  3.png
Views: 214
Size:  1.4 KB

    I don't get it... :mad:
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    (Original post by SmOgER)
    How do you integrate this: Name:  1.png
Views: 240
Size:  851 Bytes ?

    If I do it the simple way (and the only one I know), I get:
    Name:  2.png
Views: 244
Size:  3.2 KB

    yet the proper answer is TOTALLY different:

    Name:  3.png
Views: 214
Size:  1.4 KB

    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.
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    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

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    Name:  ab05776d2f7997cb326344d9199095cb.png
Views: 381
Size:  244.9 KB

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    (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:
    Show


    Name:  ab05776d2f7997cb326344d9199095cb.png
Views: 381
Size:  244.9 KB

    Do you not think all that is a trifle unnecessary even if it is a delightful shade of orange?
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    (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 *Justifying himself rapidly*
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    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



    Thanks.
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    (Original post by SmOgER)
    gosh how I hate the trigonometry...)
    :confused:

    (Original post by SmOgER)
    But now I realized that 2x/x^2 is simply = to 1/2x
    That isn't correct.
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    (Original post by SmOgER)
    gosh how I hate the trigonometry...
    what particular trigonometry do you hate?
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    (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



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