# integral using a table

• Sep 7th 2007, 12:29 PM
chocolatelover
integral using a table
Hi,

Can someone tell me if this correct, please?

int. tan^-1xdx=xtan^-1x-1/2ln(1+x^2)+c

I used the formula "tan^-1udu=utan^-1u-1/2ln(1+u^2)+c

Thank you
• Sep 7th 2007, 01:56 PM
Krizalid
Quote:

Originally Posted by chocolatelover
Hi,

Can someone tell me if this correct, please?

int. tan^-1xdx=xtan^-1x-1/2ln(1+x^2)+c

I used the formula "tan^-1udu=utan^-1u-1/2ln(1+u^2)+c

Thank you

Is it much to ask that you may use some of LaTeX or patentheses, pleaseż?

Actually, this it's solved applyin' integration by parts. Show your attempt.
• Sep 7th 2007, 01:57 PM
Jhevon
Quote:

Originally Posted by chocolatelover
Hi,

Can someone tell me if this correct, please?

int. tan^-1xdx=xtan^-1x-1/2ln(1+x^2)+c

I used the formula "tan^-1udu=utan^-1u-1/2ln(1+u^2)+c

Thank you

it's correct. please use the appropriate parentheses

EDIT: I know you were required to use an integration table to find the answer, but Krizalid may be on to something. try doing it by parts--for practice
• Sep 7th 2007, 05:00 PM
chocolatelover
Quote:

Is it much to ask that you may use some of LaTeX or patentheses, pleaseż?
Sorry. I've tried it, but I can't get it to work.
• Sep 7th 2007, 06:24 PM
topsquark
Quote:

Originally Posted by chocolatelover
Sorry. I've tried it, but I can't get it to work.

You can't get parenthesis to work???

All we ask is some way to distinguish things like sq. 1 - x^2 from sq. (1 - x^2).
-Dan
• Sep 7th 2007, 07:21 PM
Krizalid
Quote:

Originally Posted by chocolatelover
Sorry. I've tried it, but I can't get it to work.

So, you can't, let's try!

By the mythic integration by parts formula, we have that

$\displaystyle \int u\,dv=u\cdot v-\int v\,du$

We gotta integrate $\displaystyle \arctan x$

So let's take $\displaystyle u=\arctan x\implies du=\frac1{1+x^2}\,dx$ & $\displaystyle dv=dx\implies v=x$, the integral becomes to

$\displaystyle \int\arctan x\,dx=x\arctan x-\int\frac x{1+x^2}\,dx$

Now the one million dollar question: could you take it from there? :D:D

__________

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