Could someone please work me out in these problem, I did a substitution on Ln(x) but ended up with (u^2+1)/(u+1)...

here is the question find the indefinite integral of ((ln x)^2+1)/(xln(x)+3)....

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- Nov 26th 2012, 05:38 PMkspkidoEvaluating indefinite Integral
Could someone please work me out in these problem, I did a substitution on Ln(x) but ended up with (u^2+1)/(u+1)...

here is the question find the indefinite integral of ((ln x)^2+1)/(xln(x)+3).... - Nov 26th 2012, 05:48 PMProve ItRe: Evaluating indefinite Integral
Are you sure it's not instead of ?

- Nov 26th 2012, 06:40 PMkspkidoRe: Evaluating indefinite Integral
Oh I'm very sorry, it is actually (x ln x +3x)..... the 3 has 'x' with it..

- Nov 26th 2012, 06:55 PMProve ItRe: Evaluating indefinite Integral
So it is what I thought.

I would write it as .

Now this is just ONE possible substitution. I'm choosing it because I know that it will make the denominator the easiest to work with.

Let . Then your integral becomes

- Nov 26th 2012, 09:00 PMkspkidoRe: Evaluating indefinite Integral
daym... I got the u^2-6u+10/u... but at that point I didn't know what to do.. so I tried to substitute other variables.. stupid me... Thank you very much...