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int(dx)/(x(logx)^(m)) is equal to then...

`int(dx)/(x(logx)^(m))` is equal to then

A

`((logx)^(m))/(m)+C`

B

`((logx)^(m-1))/(m-1)+C`

C

`((logx)^(1-m))/(1-m)+C`

D

`((logx)^(1-m))/(m)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(1)/(x(logx)^(m))dx`
Let `log x-t rArr (1)/(x)=(dt)/(dx) rArr dx=xdx`
`therefore" "int(1)/(x(logx)^(m))dx=int(1)/(x(t)^(m))xdt int t^(-m)dt`
`=(t^(-m+1))/(-m+1)+C=((logx)^(1-m))/(1-m)+C`
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