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integration of log of x divided by square root of 1- x^2

integration of log of x divided by square root of 1- x^2

Grade:12th pass

1 Answers

Ritika Das
105 Points
5 years ago
Let u = 1-x2.
du/dx= -2x.
dx= (-1/2x).du.
So, I = ∫log x/(sqrt.(1-x2)).dx
        = ∫log x/sqrt.(u).du.(-1/2x)
        = (– log x/2x).∫u-1/2.du
        = (-log x/2x).u-1/2 + c
After replacing value of u,
I = (-log x)(sqrt.(1-x2)) + c

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