Question

Hi,
Have a completing the square integral I am trying to do and need some help getting the completing the square part down.

Answer 1

\[\int\limits (x^2-2x+1)/\sqrt{(x^2-2x+10)}\]

Answer 2

alright well do you know how to complete a square?

Answer 3

So far I have pulled Moved 10 over under the radical and replaced it with 1 so that half of the middle term squared would be the third term. Im not sure where to subtract one to make up for it though......

Answer 4

i think your supposed to subtract one from the other 1.

Answer 5

So my new equation will look like
\[\int\limits (x^2-2x+1)\div \sqrt{9+(x-1)^2}\]

Answer 6

then a tan sub?

Answer 7

YES YOUR EQUATION IS CORRECT BUT YOU NEED TO BE CAREFULLY WHEN YOU DO THE EQUATION.

Answer 8

I think I am almost done.....Im at the integral of sec^3theta-sectheta

Answer 9

OK WHEN YOU HAVE THE ANSWER JUST TEEL ME

Answer 10

I could use help with that though (;

Answer 11

Do I use the power reducing identity for sec^3(theta)?

Answer 12

YES

Answer 13

DO YOU GET THE ANSWER JANSON

Answer 14

not yet......trying to find the identity.

Answer 15

I WILL BE HERE IF YOU HAVE ANY QUESTION.

Answer 16

Are you sure I dont do sec^3 with integration by parts?

Answer 17

WELL YOU CAN DO IT BUT IT WIL HAVE MORE WORK TO DO.

Answer 18

What are you folks doing? Notice the similarity of the numerator.

\(\int\limits \dfrac{x^{2}-2x+1}{\sqrt{x^2 - 2x + 10}}\;dx = \int\limits \dfrac{(x-1)^2}{\sqrt{(x-1)^2 + 9}}\;dx\)

I found the substitution \(u^{2} = (x-1)^{2} + 9\) quite useful.

Answer 19

I KNOW THE THE SIMILARITY OF THE NUMERATOR. I JUST TRYING TO HELP HIM

Answer 20

So I found the identity but right now my integral is
\[9intSec^3\theta d\]
So when I use the power reducing indentify do I pull the constant 9 out in front of it also?
The point of the problem for me on this one is to complete the square and then use trig sub

Answer 21

YES

Answer 22

Can you help walk me through some of this last part?

Answer 23

SHOW ME THE EQUATION

Answer 24

\[9\int\limits \sec^3\theta-\sec \theta d \theta \]

Answer 25

CAN YOU HURRY UP BECAUSE I HAVE TO DO MY HOMEWORK FOR AP CHEMISTRY AND AP US HISTORY

Answer 26

its right above you...

Answer 27

As in would you show me how to do this part.

Answer 28

you dont seem to know what your doing );

Answer 29

This is Cal 3

Answer 30

its wrong.

Answer 31

IS NOT BECAUSE MY BROTHER IS HELPING ME MY FRIEND