Use integration by parts, together with the techniques of this section, to evaluate the integral. (Use C for the constant of integration.)

Question

ihannah_banana7 · Answer

$$\int\limits_{}^{}9\ln(x^2-x+12) dx$$

mathmale · Answer

Suggestion:  Factor x^2 - x + 12.
Then apply a certain property of logs.

danjs · Answer

$$\large 9 \int\limits \ln(x^2-x+12)dx$$

try letting  u=ln(x^2-x+12)      dv = dx

danjs · Answer

$$u = \ln(x^2-x+12)$$
$$du = \frac{ 2x - 1 }{ x^2 - x +12 }dx$$

dv = dx
v = x

mathmale · Answer

Dan's suggestion is a good one.

You could, alternatively, factor x^2-x+12, obtaining (x-4)(x+3).  Note that the ln of (x-4)(x+3) is ln(x-4) + ln(x+3).  You might (or might not) find this integrand easier to integrate.  Try it both ways.

danjs · Answer

@mathmale  That is a +12 on that polynomial.