INTEGRAL CALCULUS
-Integral of logarithmic functions
"Evaluate this integral of (x+3)dx/x+2

Question

anonymous · Answer

I think you'll have to use long division first since both sides have the same power. The numerator's power must be < the denominator's power.

:)

anonymous · Answer

can u answer it? i want to compare my answer.. please?

anonymous · Answer

alright, did you do the long division part?

anonymous · Answer

I got this after diving x+3 / x+2 :

1 + 1/x+2

anonymous · Answer

dividing*

anonymous · Answer

is this what you've got?

anonymous · Answer

my answer x+ln(x+2)+c is this correct?

anonymous · Answer

hold on , let me finish :)

anonymous · Answer

yes, excellent :)

anonymous · Answer

here another example can u answer this

anonymous · Answer

sure, I'll give it a try ^_^

anonymous · Answer

integral of xdx/x^2+4

anonymous · Answer

you can expand the denominator and you'll get the following:$$x/(x^2+4) = x/(x+2)^2$$

then you'll have to do the partial fractions part which is :

$$x/(x+2)^2 = A/(x+2) + B/(x+2)^2$$....etc

correct me if I'm wrong

anonymous · Answer

you know how to integrate partial fractions, right? :)

anonymous · Answer

wers the answer?

anonymous · Answer

i dont know

anonymous · Answer

lol, I have hinted the way for you for you to proceed ^_^

anonymous · Answer

yes you know :) haven't you taken partial fractions?

anonymous · Answer

oh wait

anonymous · Answer

ther's a much simpler way to do it :) hold on no need for partial fractions here

anonymous · Answer

ur answer? i want to compare my answer

anonymous · Answer

$$\int\limits_{} x/(x^2+4) dx$$

let :
$$u = x^2 +4$$
$$du = 2x dx$$

so :

$$= 1/2 \int\limits_{} 1/u du$$
$$= 1/2(\ln |u|) + c$$
$$=[ \ln|x^2+4|] /2 + c$$

sorry abt the complicated mess earlier ^_^

anonymous · Answer

is this what you've got?

anonymous · Answer

1/2ln(X^2+4)+C

anonymous · Answer

yes, well done ^_^

anonymous · Answer

i wish you can transfer your knowledge in calculus to me

anonymous · Answer

lol, I was so ignorant in it, but then worked hard to understand it. I took this in the beginning of the semester :), just be patient and practice more then you'll master it ^_^

anonymous · Answer

do you have facebook i wish we can talk together to practice my enlish

anonymous · Answer

english

anonymous · Answer

Unfortunately, I don't have FB, myspace or any of these stuff since I don't have time for them :( , I'm sorry.

anonymous · Answer

To perfect your english, read more, listen more and communicate more :) that's it

anonymous · Answer

tnx

anonymous · Answer

np :)