# Evauate the indefinite integral integrate of ((dx)/(4x^2-4x+5))

Luca B. | Certified Educator

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You should use the following formula to evaluate the given indefinite integral such that:

`int 1/(x^2+a^2) dx = (1/a) arctan (x/a) + c`

You need to convert the given form of denominator into the form presented above using the following formula `(a-b)^2 = a^2-2ab+b^2`  to complete the square in quadratic `4x^2-4x+5`  such that:

`4x^2-4x = a^2-2ab =gt {(4x^2 = a^2),(4x = 2ab):}=gt` `{(a=+-2x),(4x=2*2x*b):}` `=> b = 1`

Hence, you need to add and subtract 1 such that:

`4x^2 - 4x + 1 - 1 = (2x - 1)^2 - 1`

`4x^2 - 4x + 5 = (2x - 1)^2 - 1 + 5`

`4x^2 - 4x + 5 = (2x - 1)^2 + 4`

You need to...

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