How do you integrate $\frac{5 ln (x)}{x^{7}}$ $(5 ln(x))/x^(7)$ ?

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Answer 1 · 2018-05-13T17:07:31

The answer is $= - \frac{5}{6} \frac{ln x}{x^{6}} - \frac{5}{36 x^{6}} + C$ $=-5/6lnx/x^6-5/(36x^6)+C$

$intuv'=uv-u'v$

The integral is

$I=int(5lnxdx)/x^7=5int(lnx)/x^7$

$u=lnx$ , $=>$ , $u'=1/x$

$v'=x^-7$ , $=>$ , $v=-1/(6x^6)$

Therefore,

$I=-5/6lnx/x^6+5/6int(dx)/x^7$

$=-5/6lnx/x^6-5/(36x^6)+C$

How do you integrate (5 ln(x))/x^(7)5ln(x)x7(5 ln(x))/x^(7)?