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Question

How do you evaluate the integral(x-1)(x+1)dx ?


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Solution

Step 1: Split the integrating function:

(x-1)(x+1)dx

=x+1-2(x+1)dx=x+1x+1-2x+1dx=1-2x+1dx

Step 2: Integrate the function using the linearity property.

1-2x+1dx=dx-2x+1dx=x-21x+1dx....................(1)

Let x+1=u

dx=du

Thus,

1x+1dx=1udu=lnu=lnx+1 1xdx=lnx

Substitute the value in equation 1,

1-2x+1dx=x-2lnx+1+c

Hence, the value of (x-1)(x+1)dx is x-2lnx+1+c.


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