Maharashtra State BoardHSC Commerce 12th Board Exam
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Evaluate: ∫dx/25x-x(logx)2 - Mathematics and Statistics

Sum

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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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.3 | Page 139
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