## Math question

I usually don’t need to ask these any more, but I’m not seeing how one step proceeds to the next.

xln(2x+1) – x + 1/2ln(2x+1) + C

becomes, in the solutions manual:

1/2(2x+1)ln(2x+1) – x + C

Where did the x go? How is it that ln is only in front of one of the (2X+1) terms? How did it go from adding to multiplying? ln rule of lnx+lny = lnxlny, but why is there only an ln in front of one of the terms? What hte heck happened there? Thanks. Come with me if you want to live
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### 13 Responses to Math question

1. Ryu says:

Well,
xln(2x+1) = ln (2x+1)^x
and
.5ln(2x+1) = ln (2x+1)^.5
so add those terms.
and
1/2 (2x+1) = x + 1/2
Looks like they just combined terms and moved the exponent back in front.

• mindweapon says:

Still not seeing it. How do you add:

xln(2x+1) = ln (2x+1)^x
and
.5ln(2x+1) = ln (2x+1)^.5?

Wouldn’t you get ln(2x+1)^.5+x?

Where did the x go? Why is ln only on one of the terms and not the other?

2. Steve Johnson says:

Easy once you look at it as an equation.

x ln(2x+1) – x + 1/2 ln(2x+1) + C = 1/2 (2x+1) ln(2x+1) – x + C

+ x – C to both sides

x ln(2x+1) + 1/2ln(2x+1) = 1/2(2x+1)ln(2x+1)

Factor out a ln(2x+1)

(x + 1/2) ln (2x+1) = 1/2(2x+1) ln(2x+1)

Multiply the left side by 2/2

1/2*2(x+1/2) ln (2x+1) = 1/2(2x+1) ln(2x+1)

1/2(2x+1) ln (2x+1) = 1/2(2x+1) ln(2x+1)

• mindweapon says:

Thanks Steve, and Ryu. I’m going to have to study this pretty closely, but you guys spelled it out as good as it’s going to be spelled out.

3. Piotr says:

xln(2x+1) – x + 1/2ln(2x+1) + C = [ln(2x + 1)] (x + 1/2) – x + C = 1/2(2x+1)ln(2x+1) – x + C

• Piotr says:

ab – x + db + C = (a+d)b – x + C

• mindweapon says:

Spasibo, Piotr.

4. FD says:

Why doesn’t the book leave it as (x+1/2)ln(2x+1) – x + C? Is the next step integration by parts?

• mindweapon says:

No, that’s the final answer.

5. countenance says:

Look at all ths right wing ignorance on parade.

I bet this equation is for making some sort of secret potion that takes away the ability for black people to build pyramids and be kings and queens.

• mindweapon says:

Shhh, dont’ give away our secret!

• countenance says:

You mean I’m not supposed to say that this is the secret formula for making black men impotent?

Moral of this story: NEVER trust me with secrets.

• mindweapon says:

Damn, you are destroying all our evil plans!