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C4 integration

Can anyone explain to me why the integral of b) :

ImageUploadedByStudent Room1393090846.805701.jpg

Is this:

ImageUploadedByStudent Room1393090919.421831.jpg

Confused as to how to get there. Any help would be much appreciated!


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Reply 1
They changed it into index form so it would be (2x+1)2(2x+1)^{-2} and now you'd apply the inverse chain rule.
*int* 1/(2x+1)^2

Identical to

(2x+1)^-2

Add one to power

(2x+1)^-1

Now if you differentiated that you'd have -2 extra so divide by that -2

-1/2 (2x+1)^-1

Remember to add constant

And simplify
What about ln?

EDIT: Nevermind those are for equations that aren't squared or greater.
Original post by ModernScholar
What about ln?


What about it?

Because it's 1/(ax+b)^n

If n is 2 or bigger, you'd use inverse chain rule, ln would be a looong route
Reply 5
Original post by Dilzo999
They changed it into index form so it would be (2x+1)2(2x+1)^{-2} and now you'd apply the inverse chain rule.


Ohhh yeah, can't believe I didn't spot that. Thanks!


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Original post by L'Evil Fish
What about it?

Because it's 1/(ax+b)^n

If n is 2 or bigger, you'd use inverse chain rule, ln would be a looong route


I know, I worked it out a few moments later and edited my post.

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