Maharashtra State BoardHSC Commerce 12th Board Exam
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Evaluate: ∫dxx[(logx)2+4logx-1] - Mathematics and Statistics

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Sum

Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`

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Solution

Let I = `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`

Put log x = t

∴ `1/"x" "dx" = "dt"`

∴ I = `int "dt"/("t"^2 + 4"t" - 1)`

`= int 1/("t"^2 + 4"t" + 4 - 4 - 1)`dt

`= int 1/(("t + 2")^2 - 5)` dt

`= int 1/(("t + 2")^2 - (sqrt5)^2)` dt

`= 1/(2 sqrt5) log |("t" + 2 - sqrt5)/("t" + 2 + sqrt5)|` + c

∴ I = `1/(2 sqrt5) log|(log"x" + 2 - sqrt5)/(log "x" + 2 + sqrt5)|` + c

Concept: Methods of Integration: Integration by Parts
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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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