Maharashtra State BoardHSC Commerce 12th Board Exam
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Evaluate: ∫12x+3xlogx dx - Mathematics and Statistics

Sum

Evaluate: `int 1/(2"x" + 3"x" log"x")` dx

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Solution

Let I = `int 1/(2"x" + 3"x" * log"x")` dx

`= int 1/("x"(2 + 3 log "x"))` dx

Put 2 + 3 log x = t

∴ `3 * 1/"x" "dx"` = dt

∴ `1/"x"  "dx" = 1/3  "dt"`

∴ I = `1/3 int 1/"t" * "dt"`

`= 1/3` log |t| + c

∴ I = `1/3` log |2 + 3 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 4.2 | Page 138
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