nightmare integral

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April 19th 2008, 06:03 PM
ArmiAldi

nightmare integral

(Sweating)Find the integral.
1/(x(ln(x))^7)dx
April 19th 2008, 06:05 PM
polymerase

Quote:

Originally Posted by ArmiAldi

(Sweating)Find the integral.
1/(x(ln(x))^7)dx

just let $u=\ln x$

$u=\ln x\;du=\frac{dx}{x}$

$\int \frac{dx}{x\ln^7 x}=\int \frac{du}{u^7}=-\frac{1}{6u^6}$

Thus, $\int \frac{dx}{x\ln^7 x}=-\frac{1}{6\ln^6x}+C$

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