If the integration of (lnx) ^2=x[f(x)]^2+Ax[f(x)-1]+c , then

Answers (1)

Solution: We have ,

               I=int (ln x)^2dx=x[f(x)]^2+Ax[f(x)-1]+c

         \Rightarrow I= int (ln x)^2dx=int (ln x)^2	imes 1\ \Rightarrow I=x(ln x)^2-2int (ln x)	imes 1 hspace0.1cmdx\ \Rightarrow I=x(ln x)^2-2x[(ln x)-1]+c\ \Rightarrow f(x)=ln x,andhspace0.2cmA=-2.

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