Question

how to solve the above question please explain me with steps​

Answer 1

Step-by-step explanation:

we have,

$\int log_{5}(x) dx$

$= > \int log_{5}(x) .1 \: dx$

$= > log_{5}(x) \int dx - \int ( \frac{d}{dx} log_{5}(x) .\int dx)dx$

$= > x log_{5}(x) - \int \frac{1}{x \: ln(5)} .x \: dx$

$= > x \: log_{5}(x) - x.log_{5}(e) + c$

$= > x( log_{5}(x) - log_{5}(e) ) + c$

$= > x( \frac{ ln(x) - 1}{ ln(5) }) + c$