OpenStudy (konradzuse):

Find the integral 1 ---- x(ln(x))^6

6 years ago
OpenStudy (konradzuse):

I guess we could start out with \[x^-1 * (\ln(x))^{-6}\]

6 years ago
OpenStudy (anonymous):

better: \[\ln(x)^{-6}/x\] and solve by substitution

6 years ago
OpenStudy (konradzuse):

or actually keep it as 1/x for the du

6 years ago
OpenStudy (konradzuse):

u = ln(x) du = 1/x dx

6 years ago
OpenStudy (anonymous):

yes

6 years ago
OpenStudy (konradzuse):

so it's going ot be u^-6 du

6 years ago
OpenStudy (konradzuse):

nice! :D

6 years ago
OpenStudy (konradzuse):

\[\frac{u^{-5}}{5} + c?\]

6 years ago
OpenStudy (konradzuse):

\[\frac{(\ln(x))^{-5}}{5} + c?\]

6 years ago
OpenStudy (anonymous):

don't forget - sign

6 years ago
OpenStudy (konradzuse):

\[-\frac{(\ln(x))^{-5}}{5} + c?\]

6 years ago
OpenStudy (anonymous):

yes

6 years ago
OpenStudy (konradzuse):

Been doing stupid stuff like that all day... Have the worst headache :(

6 years ago
OpenStudy (anonymous):

:)

6 years ago
OpenStudy (konradzuse):

:D

6 years ago