Integrate (x^2+4)/(x+2)
Leave answer as integral in terms of u.

Question

Integrate (x^2+4)/(x+2)
Leave answer as integral in terms of u.

myininaya · Answer

have you tried diving the integrand?

solomonzelman · Answer

$\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{x^2+4}{x+2}dx}$     is same as,   $\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{(x+2)(x-2)}{x+2}dx}$

I am not sure why you need a "u" here....

solomonzelman · Answer

just cancel things out, and integrate term by term....

myininaya · Answer

x^2-4=(x+2)(x-2)
x^2+4=(x+2i)(x-2i)

solomonzelman · Answer

ooops

solomonzelman · Answer

yes, the second I put that, I was like nope... sorry

$\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{x^2+4}{x+2}dx}$

solomonzelman · Answer

try to make the denominator a signle term (using u substitution)

solomonzelman · Answer

*single   term

solomonzelman · Answer

what would your "u" be?

anonymous · Answer

u=x+2

myininaya · Answer

oh wait 
are we not suppose to integrate?
it says leave integrals in terms of u...
I guess if that is so let u=x+2 then du=dx
and blah blah

anonymous · Answer

Would you rewrite as (x^2+4)(x+2)^-1

myininaya · Answer

put still it doesn't say put the integrand in a form that is integrateble

myininaya · Answer

weird question

myininaya · Answer

but (not put)

solomonzelman · Answer

(As I just showed I suck, lol, but)
You can would need to integrate, I guess.

solomonzelman · Answer

I mean just need.

myininaya · Answer

well it says "leave answer as integral in terms of u"

myininaya · Answer

it doesn't say integrate

myininaya · Answer

it just says to convert $$\int\limits_{}^{}f(x) dx \text{ to } \int\limits_{}^{}g(u) du$$

myininaya · Answer

and if that is so then you can use any substitution (useless or not)

ganeshie8 · Answer

guess these divisions always have shortcuts $$\frac{x^2+4}{x+2} =  \dfrac{(x^2-4)+8}{x+2}  =  x-2 + \frac{8}{x+2}$$

i feel "answer" refers to integrate, i also feel the OP is hiding some details of actual problem hmm

solomonzelman · Answer

magic zero, I sometimes refer to what ganeshie just did. I like that.

solomonzelman · Answer

Idk if you have to integrate or not, but again, I think you would still need to.
This is calculus afterall, not just an algebraic substitution technique.

ganeshie8 · Answer

@phanta1  say something.. what does $u$ refer to here ? if psble please take a screenshot of actual problem and attach

myininaya · Answer

lol I just noticed my first posting says diving instead dividing