What is the integral of

Question

1/(x^2 + 8x + 17)^2?

Answer 1

The function is 

Rewriting it as 

=

Assume (x  + 4 ) = tan x ,

 =       []

Now 

=

Rewriting  as 

Since sin(2A) = 2 sinA cosA

 The value of sin 2x is   

Now substituting the  values   the integral becomes 

Now  Replacing the values  we get,

Hence, the integral is

 .