# Thread: Integral Problem - Power of n

1. ## Integral Problem - Power of n

this is my answer using integration by parts

2. ## Re: Integral Problem - Power of n

I multiplied each side by (a + bu) and I got this

on the left side, I have this

then I can move one term to the right side and I add the constants and I got

but I should get this to have the correct answer

Where did I go wrong?

3. ## Re: Integral Problem - Power of n

Can anyone help me in this integral? I really wanna know where did I miss the negative sign!

4. ## Re: Integral Problem - Power of n

Stop yelling!!!

-Dan

5. ## Re: Integral Problem - Power of n

Originally Posted by joshuaa
I multiplied each side by (a + bu) and I got this

...

Where did I go wrong?
multiplying each side by (a+b u) where u is the variable of integration is not a valid operation

6. ## Re: Integral Problem - Power of n

(a + bu) / (a + bu) = 1, where (a + bu) does not equal zero.

I don't see why it is not valid cuz I am just multiplying by one!

7. ## Re: Integral Problem - Power of n

if I am not mistaken what you are saying is

$\displaystyle (a+b u)\int \frac{1}{u^n\sqrt{a+b u}} \, du\overset{\text{??}}{=}\int \frac{a+b u}{u^n\sqrt{a+b u}} \, du$

8. ## Re: Integral Problem - Power of n

I did not put any variable outside the integral!

take (a + bu) inside the integral, then yeah that what I meant

9. ## Re: Integral Problem - Power of n

Originally Posted by joshuaa
I did not put any variable outside the integral!

take (a + bu) inside the integral, then yeah that what I meant
Then where did the a + bu go inside the integral? I'm only seeing the one that Idea noted.

-Dan

10. ## Re: Integral Problem - Power of n

My bad. It seems that you are both correct.

topsquark and Idea, thanks for passing by and spending some time in this thread.

I think that it is the time to close up the thread.

11. ## Re: Integral Problem - Power of n

Originally Posted by joshuaa
I think that it is the time to close up the thread.
Agreed.