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Evaluate the integral integrate of ((x-2)/(2x^2+7x+3))dx

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lfryerda eNotes educator | Certified Educator

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To evaluate the integral, we need to use partial fractions on the integrand.  This means that:



`=a/{2x+1}+b/{x+3}`   now use method of comparing coefficients


The constant terms give

`-2=3a+b`   equation (1)

The linear terms give

`1=a+2b`   equation (2)

Now subtract (2)-2x(1)


so a=-1

Then we get b=1

This means the integral becomes:



`=-1/2ln(2x+1)+ln(x+3)+C`  where C is the constant of integration


The integral evaluates to `ln({x+3}/(2x+1)^{1/2})+C` .

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