Question

integration by parts : log (x^2-5x+6)dx​

Answer 1

Answer:

x^2–5x+6 can be written as (x-2)(x-3). Now the properties of logarithms states that ln(ab)=lna+lnb. Therefore ln(x^2–5x+6)=ln((x-2)(x-3))=ln(x-2)+ln(x-3).

We know that integral lnxdx=xlnx-x+c(this could be obtained by using uv rule of integration). Therefore integral ln(x-2)+ln(x-3)=(x-2)ln(x-2)-(x-2)+c1+(x-3)ln(x-3)-(x-3)+c2=(x-2)ln(x-2)-(x-2)+(x-3)ln(x-3)-(x-3)+c .

Step-by-step explanation:

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