# Reduction formula

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