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

- anonymous

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

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- anonymous

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

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

- anonymous

alright, did you do the long division part?

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## More answers

- anonymous

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

- anonymous

dividing*

- anonymous

is this what you've got?

- anonymous

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

- anonymous

hold on , let me finish :)

- anonymous

yes, excellent :)

- anonymous

here another example can u answer this

- anonymous

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

- anonymous

integral of xdx/x^2+4

- anonymous

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

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

- anonymous

wers the answer?

- anonymous

i dont know

- anonymous

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

- anonymous

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

- anonymous

oh wait

- anonymous

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

- anonymous

ur answer? i want to compare my answer

- anonymous

\[\int\limits_{} x/(x^2+4) dx\]
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

is this what you've got?

- anonymous

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

- anonymous

yes, well done ^_^

- anonymous

i wish you can transfer your knowledge in calculus to me

- anonymous

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

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

- anonymous

english

- anonymous

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

- anonymous

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

- anonymous

tnx

- anonymous

np :)

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