Question

Evaluate:

`∫ log_10 "x dx"`

Answer 1

Given: `∫ log_10 "x dx" = int (log_"e" "x")/(log_"e" 10) "dx"`

= `1/(log_"e" 10) int log_"e" "x". 1 "dx"`

On integrating by parts, we get

= `1/(log_"e" 10) [log_"e" "x". "x" - int 1/"x". "x dx"] + "c"`

= `1/(log_"e" 10) ("x" log_"e" "x" - "x") + "c"`

= x(log_e x − 1). log₁₀ e + c