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Question
Evaluate:
`∫ log_10 "x dx"`
Solution
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(loge x − 1). log10 e + c
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