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

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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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Deependra Verma

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