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Aparna Tiwari Grade: 12
        

Integrate:-


{(1/(logx))-(1/(logx)2)} for upper limit e2 and lower limit 0.

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

I = {1/logx -1/(logx)2 }dx


multiply numerator & denominator by x


I = x{1/logx-1/(logx)2}dx /x


put logx = t


    dx/x = dt      & x=et


now


        I = et{1/t - 1/t2}dt       


        I = et{ f(t) + f1(t) }


we have a direct formula for ex{f(x) + f1(x)}dx = exf(x)


 so I = et f(t) 


        =et/t = (x / logx)       lim 0 to e2


        =0 - e2/2

6 years ago
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