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Question
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
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Solution
Let I = `int "dx"/(25"x" - "x"(log "x")^2)`
`= int 1/("x"[25 - (log "x")^2])` dx
Put log x = t
∴ `1/"x"` dx = dt
∴ I = `int "dt"/(25 - "t"^2)`
`= int 1/((5)^2 - "t"^2)` dt
`= 1/(2(5)) * log |(5 + "t")/(5 - "t")|` + c
∴ I = `1/10 log |(5 + log "x")/(5 - log "x")|` + c
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