How do I find the integral $intx/(x-6)dx$ ?

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Answer 1 · 2014-09-30T02:00:46

By Substitution,

$int x/{x-6}dx=x+6ln|x-6|+C$

Let us look at some details.

$int x/{x-6}dx$

by the sunstitution $u=x-6$ ,
$Rightarrow x=u+6$
$Rightarrow dx=du$

$=int {u+6}/u du$

by splitting the integrand,

$=int (1+6/u) du$

$=u+6ln|u|+C_1$

by putting $u=x-6$ back in,

$=x-6+6ln|x-6|+C_1$

by letting $C=C_1-6$ ,

$=x+6ln|x-6|+C$

I hope that this was helpful.

How do I find the integral intx/(x-6)dxintx/(x-6)dx ?