Integration by completing the square

[luigihs]

1/x^2 + 4x + 5



1) Completing the square
x^2 + 4x/2 + 5 - 4
(x+2)^2 +1

After this I know what to do??

 

[Mark44]

1/x^2 + 4x + 5
1) Completing the square
x^2 + 4x/2 + 5 - 4
(x+2)^2 +1

After this I know what to do??

What's your question? You're asking about an integration problem - what is the problem?

x² + 4x + 5 = x² + 4x + 4 + 1 = (x + 2)² + 1

 

[HallsofIvy]

What you wrote is
$$\frac{1}{x^2}+ 4x+ 5$$
but I feel sure you meant
$$\frac{1}{x^2+ 4x+ 5}= \frac{1}{(x+2)^2+ 1}$$

Now, do you know an integral formula for
$$\int \frac{dx}{x^2+a^2}$$?

 

[Mark44]

I misread that 1/ part as "problem #1". Didn't occur to me that he meant the reciprocal of something.