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Question

1-2121-x1+x2+1+x1-x2-2dx


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Solution

Step 1. Integrate the given equation:

1-2121-x1+x2+1+x1-x2-2dx

=1-2121-x1+x-1+x1-x2dx a2+b2-2ab=(a-b)2

=20121-x1+x-1+x1-x2dx

=20121+x2-2x-1-x2-2x1-x2dx

=2012-4x1-x2dx ……(1)

Let 1-x2=t

Step 2. Differentiate it with respect to x

-2xdx=dt

dx=dt-2x

Step 3. Put the value of dx and 1-x2 in equation (1), we get

4112dtt

4logt112 1xdx=logx

4log12-log1

4log12 logA-logB=logAB

Hence, the integration of given equation is 4log12


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