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Grade: 12
        

Integrate:-


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

7 years ago

Answers : (1)

vikas askiitian expert
509 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

7 years ago
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