please help with this problem- i've been working for the last 2 hours and can't seem to find a solution

the integral of ln(x^2-x+2)

I "cheated"

I went to

http://integrals.wolfram.com/index.jsp?expr=ln(x^2+-+x+%2B+2)&random=false

Sure! To find the integral of ln(x^2 - x + 2), one approach is to use integration by parts. Integration by parts is a technique that allows us to split the integral of a product of two functions into two simpler integrals.

The general formula for integration by parts is:

∫ (u * dv) = u * v - ∫ (v * du)

In this case, let's choose u = ln(x^2 - x + 2) and dv = dx. We can then differentiate u to find du and integrate dv to find v.

To compute du, we can use the chain rule. The derivative of ln(x^2 - x + 2) with respect to x is given by:

du = (1 / (x^2 - x + 2)) * (2x - 1) dx

To compute v, we can integrate dv, which is simply dx:

v = ∫ dx = x

Now we can use the formula above to find the integral:

∫ ln(x^2 - x + 2) dx = u * v - ∫ v * du
= ln(x^2 - x + 2) * x - ∫ x * (1 / (x^2 - x + 2)) * (2x - 1) dx

Now we have a simpler integral to evaluate:

∫ x * (1 / (x^2 - x + 2)) * (2x - 1) dx

We can simplify this integral further by multiplying out the terms in the numerator and expanding the denominator.

After simplifying, you can try using partial fraction decomposition or substitution techniques to evaluate the integral and find the solution.