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# Integration by Subsitution watch

1. Sorry! I'm just struggling with a few questions, I've tried doing them like 10 times and I seem to be getting a close, but not the same answer. So if anyone could do even just one, and do each step for me I'd totally love you forever =D xxx

∫ 5x / 5x-2 dx u = 5x-2

∫ x / (2x-1)3dx u = 2x-1

∫ x / √(x2-1)
2. (Original post by -x-buttercup-x-)
Sorry! I'm just struggling with a few questions, I've tried doing them like 10 times and I seem to be getting a close, but not the same answer. So if anyone could do even just one, and do each step for me I'd totally love you forever =D xxx

∫ 5x / 5x-2 dx u = 5x-2

∫ x / (2x-1)3dx u = 2x-1

∫ x / √(x2-1)

first one:

u = 5x-2
du/dx = 5
dx/du = 1/5
dx = du/5

∫ 5x / 5x-2 dx
= (1/5)∫ ((u+2)/u) du
= (1/5)∫(1+2/u) du
= (1/5)(u+2lnu)+c
= (5x-2)/5 + (2/5)ln(5x-2) + c
= x + (2/5)ln(5x-2) + k (k = c-2/5)

Im not really sure with the second one, the 3 is confusing me is it ∫ (x / 3(2x-1))dx ?
3. ∫ x / √(x2-1)
∫ x / √(x²-1) dx if thats what you ment then let
u=x²-1 => x²=u+1 => x=(u+1)1/2
du/dx=2x = 2(u+1)1/2
dx=du/2(u+1)1/2

∫ (u+1)1/2 / (u1/2)2(u+1)1/2 du
=∫ 1/(2u1/2) du
=∫(1/2)u-1/2 du
=u1/2+c
=(x²-1)1/2 +c
4. Thankyou both of you =D You'll be getting pos rep shortly =D xxx
5. oh and yep I did mean x squared, it did come up right in word, but most of gone funny when I pasted it into here sorry x
6. (Original post by -x-buttercup-x-)
∫ x / (2x-1)3dx u = 2x-1
Assuming you mean ^3
x =(u+1)/2
dx/du = u/2

1/4 ∫ (u+1)u/u3 du
1/4 ∫(u+1)/u2 du
1/4 ∫1/u + 1/u2 du
1/4 [ lnu - 1/u ] + C
7. (Original post by YYYY)
Assuming you mean ^3
x =(u+1)/2
dx/du = u/2

1/4 ∫ (u+1)u/u3 du
1/4 ∫(u+1)/u2 du
1/4 ∫1/u + 1/u2 du
1/4 [ lnu - 1/u ] + C
dx/du = 1/2 surely?

1/4 ∫ (u+1)/u3 du
1/4 ∫1/u2 + 1/u3 du
-1/4[1/3u-3 + 1/4u-4 + c]

-----------------------------------------------------

EDIT: MY METHOD WAS WRONG FOR THIS ONE. you can use x = sec u, but i can't be bothered to go through it. if you have a formula book, it's nice and simple, otherwise i'd use the substitution shown earlier.
8. (Original post by sea tea)
dx/du = 1/2 surely?

1/4 ∫ (u+1)/u3 du
1/4 ∫1/u2 + 1/u3 du
-1/4[1/3u-3 + 1/4u-4 + c]
****!
My mistake
9. Awww thanks again, I actually understand it now.I will rep you all as soon as I can

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Updated: April 11, 2006
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