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To find
we do a perfect square factorisation to get
We can solve using partial fractions. We should find values A and B such that
We multiply all of this by the denominator of the LHS to get
Now, if we let x=1, we get 1=2B, or B=1/2. Now, let x= –1 to get 1= –2A or A= –1/2. This gives us
The graph of the integrand and the answer look like this:

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Next page : The integral of one over x^2+1
