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# An intergration problem watch

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1. How Do you intergrate 10/(3+2x)squared

i am all confused at the moment as my brain has stopped working.
2. (Original post by foreverblue)
How Do you intergrate 10/(3+2x)squared

i am all confused at the moment as my brain has stopped working.
If you differentiate the bottom bit, you get 2. Using the rule that the integral of f'(x)/f(x)=lnf(x) + c and the top is 5 times f'(x), we have:
INT 5f'(x)/f(x)=5ln(3 + 2x) +c

EDIT: This is wrong. Note to self - read the question before answering to prevent looking foolish.
3. (Original post by foreverblue)
How Do you intergrate 10/(3+2x)squared

i am all confused at the moment as my brain has stopped working.
it's 10(3+2x)^-2 so integrated that would be -5(3+2x)^-1 as it's a function of a function so you need to take the differential of the bracket into account.

EDIT: That's -5/(3+2x)
4. (Original post by meepmeep)
If you differentiate the bottom bit, you get 2. Using the rule that the integral of f'(x)/f(x)=lnf(x) + c and the top is 5 times f'(x), we have:
INT 5f'(x)/f(x)=5ln(3 + 2x) +c
wouldn't the 'squared' make any difference?
5. (Original post by mockel)
wouldn't the 'squared' make any difference?
Yes it does, if it was a ln, then the bottom (3+2x)^2 is differentiated for the top, giving the top as 2(3+2x), which is not what you get. I think he just forgot the square, easy mistake to make, I do it as well and I really hope I won't do it tomorrow
6. (Original post by mockel)
wouldn't the 'squared' make any difference?
Oops. Didn't see the squared. Must read the question....

Anyway, if that's the case....

Use integration by substitution. Let 3+2x=u
Thus, x=(u-3)/2 so dx/du=1/2 so dx=du/2

Thus integral of 10/(3+2x)^2dx= integral of 5/u^2 = -5u^-1+C
=-5/(3+2x) + c
7. (Original post by meepmeep)
Oops. Didn't see the squared. Must read the question....

Anyway, if that's the case....

Use integration by substitution. Let 3+2x=u
Thus, x=(u-3)/2 so dx/du=1/2 so dx=du/2

Thus integral of 10/(3+2x)^2dx= integral of 5/u^2 = -5u^-1+C
=-5/(3+2x) + c
Must read the question is what was hissed at me fiercely before my physics practical exam. Apparently I am god's gift to not reading questions
8. (Original post by Mysticmin)
Must read the question is what was hissed at my fiercely before my physics practical exam. Apparently I am god's gift to not reading questions
And I keep doing "Andrew specials" as they're now called (not by me though) which is basically doing all the hard parts right then do something completely stupid at the end (eg. 1/4+4=5/4).

Awww, just realised, I've gone and missed my thousandth post.
9. (Original post by Mysticmin)
it's 10(3+2x)^-2 so integrated that would be -5(3+2x)^-1 as it's a function of a function so you need to take the differential of the bracket into account.

EDIT: That's -5/(3+2x)
So when integrating something similar to the question given above, i not only divide by the original power plus one, but also the DIFFERENTIAL of the funtion underneath - is that right?
10. (Original post by Silly Sally)
So when integrating something similar to the question given above, i not only divide by the original power plus one, but also the DIFFERENTIAL of the funtion underneath - is that right?
Correct
11. (Original post by meepmeep)
And I keep doing "Andrew specials" as they're now called (not by me though) which is basically doing all the hard parts right then do something completely stupid at the end (eg. 1/4+4=5/4).

Awww, just realised, I've gone and missed my thousandth post.
Damn, well have a theoretical chocolate cake complete with a thousand lit candles from me

I always mess up the easy bits, I switch off when I do them. You're called andrew too? Why is it all the andrews I meet do double maths... Must be the name.
12. (Original post by foreverblue)
How Do you intergrate 10/(3+2x)squared

i am all confused at the moment as my brain has stopped working.
∫ ² ³ ± ÷ ° √ ∂ ∞ ≈ ≠ ≡ ≥ ≤ ø Ø ½ ¼ « » µ π

Or if you want to keep it very simple, take the 10 outside of the integral:

10∫ 1/(3+2x)^2 dx and integrate:

10 * -((3+2x)^-1)/2) = -5(3+2x)^-1 + c
13. (Original post by Mysticmin)
Correct
YAY thanks!!!

So if the power is more than or less than one, i basically put it on the top line and make it a -ve power and then take it from there.

Also one other question, suppose if the question was something like:

INT 10/[(2x^2 - 3x +1)^2]

[-10(4x - 3)]/[(2x^2 - 3x +1] ????

This is a made up question that i thought of btw
14. (Original post by Silly Sally)
YAY thanks!!!

So if the power is more than or less than one, i basically put it on the top line and make it a -ve power and then take it from there.

Also one other question, suppose if the question was something like:

INT 10/[(2x^2 - 3x +1)^2]

[-10(4x - 3)]/[(2x^2 - 3x +1] ????

This is a made up question that i thought of btw
No, as the x's on top can't dissapear. I'm sorry, You can only do that when the bracket differentiates to give an integer

With your above question, you'd need to partial fraction the function before integrating.
15. (Original post by Mysticmin)
No, as the x's on top can't dissapear. I'm sorry, You can only do that when the bracket differentiates to give an integer

With your above question, you'd need to partial fraction the function before integrating.
cant you expand it and then 10 divided by the coefficients of the equation then differentiate it
16. (Original post by Mysticmin)
No, as the x's on top can't dissapear. I'm sorry, You can only do that when the bracket differentiates to give an integer

With your above question, you'd need to partial fraction the function before integrating.
Oh dear, I wonder how silly sally feels. Who ever said maths was easy? Why can't we get nice questions. Oh well.
17. (Original post by Mysticmin)
No, as the x's on top can't dissapear.
What do you mean by this statement?

Ok - i PROMISE the last question!!!

suppose if you have an x at the top before you integrate so for example - here's another of my made up examples!!! :

INT x/(10-3x)^3

(x/6)/(10 - 3x)^2 ???

Or wouldn't it work?

Thanks!!!

I will give you a rep for all your help - but you will have to wait for a while until the 24hr rule has expired!!!
18. (Original post by Bhaal85)
Oh dear, I wonder how silly sally feels. .
Awful? Terrible? Nearly close to tears? Suicidal?

Oh NO!!! - Those are just an understatement at the moment!!!
19. (Original post by Silly Sally)
What do you mean by this statement?

Ok - i PROMISE the last question!!!

suppose if you have an x at the top before you integrate so for example - here's another of my made up examples!!! :

INT x/(10-3x)^3

(x/6)/(10 - 3x)^2 ???

Or wouldn't it work?

Thanks!!!
Anyone???

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