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I really have no clue where to get started with this integral. Any help would be appreciated.

Evaluate the indefinite integral.

integrate of ln(x^2+10x+24)dx

With the ln() function, it is known that ln(ab) = ln(a) + ln(b).

Since x²+10x+24 factors into (x+4)(x+6), this means

ln(x²+10x+24) = ln[(x+4)(x+6)] = ln(x+4) + ln(x+6).

It is known that integral os ∫ln(x+4) + ln(x+6)dx =

∫ln(x+4)dx + ∫(ln(x+6)dx = 1/(x+4) + 1/(x+6) + C.

Calculus

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