# Math Help - integrate this?

1. ## integrate this?

how would i integrate

$\int \frac{dx}{4x^{2}-4x +17}$

2. Originally Posted by birdman22
how would i integrate

$\int \frac{dx}{4x^{2}-4x +17}$
When dealing with a reciprocal quadratic you either need to complete the square or factorise.

In this case you need to complete the square.

you should get $\int \frac{dx}{(2x-1)^2 +4^2}$

now use the substitution $2x-1 = 2 \tan u$

give this a shot on your own and see how it goes.

For checking purposes only, the answer is $\frac{1}{8} \arctan \left( \frac{2x - 1 }{4} \right)$.

Bobak