Reduction formula

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September 2nd 2008, 10:04 PM
symstar

Reduction formula

I need to use the reduction formula for this problem.
$\int(\ln{x})^{n} dx$ where $n\geqslant{2}$

Would these be the best choices for the integration?
$u=(\ln{x})^{n-1}$
$du=(\tfrac{1}{x})(n-1)(\ln{x})^{n-2} dx$
$dv=\ln{x} dx$
$v=x\ln{x}-x$
September 2nd 2008, 10:22 PM
mr fantastic

Quote:

Originally Posted by symstar

I need to use the reduction formula for this problem.
$\int(\ln{x})^{n} dx$ where $n\geqslant{2}$

Would these be the best choices for the integration?
$u=(\ln{x})^{n-1}$
$du=(\tfrac{1}{x})(n-1)(\ln{x})^{n-2} dx$
$dv=\ln{x} dx$
$v=x\ln{x}-x$

No.

Let $I_n = \int (\ln x)^{n} \, dx$ .

Use the choice $u = (\ln x)^{n}$ and $dv = dx$ .

Then $I_n = x \, (\ln x)^n - n I_{n-1} \, ....$

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