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Question
Verify the following:
`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`
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Solution
L.H.S. = `int (2x + 3)/(x^2 + 3x) "d"x`
Put x2 + 3x = t
∴ (2x + 3) dx = dt
⇒ `int "dt"/"t" = log |"t"|`
⇒ `log |x^2 + 3x| + "C"` = R.H.S.
L.H.S. = R.H.S.
Hence verified.
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