Question

Integration of 1/x^2(1/x)dx when u=-1/x​

Answer 1

Step-by-step explanation:

We have,

$\int (\frac{1}{ {x}^{2} } )( \frac{1}{x} )dx$

$let \: u = - \frac{1}{x} \\ du = \frac{1}{ {x}^{2} } dx$

$\int( - u)du$

$= - \int \: udu$

$= - \frac{ {u}^{2} }{2} + c$

$= - \frac{ (- \frac{1}{x})^{2} }{2} + c$

$= - \frac{1}{2 {x}^{2} } + c$