Posted by Paul on .
Evaluate the following definite integral:
integral at a = 1, b=2
4dx/(9x^2+30x+25)
Would I have to separate them in 3 terms as:
4 ∫1/9x^2 + ∫1/30x + ∫1/25
resulting in: 4/(3x^3)+ (15x^2)+ C?
and from there I can replace a and b
f(a)  f(b)?
Thank you

Calculus 
Steve,
Booo!
1/(a+b+c) is NOT 1/a + 1/b + 1/c
What you need to do is let
u = 3x+5 and you have
du = 3 dx, so dx = du/3
x in [1,2] means u in [2,11]
giving you
∫[2,11] 4/u^2 du/3
4/3 ∫[2,11] u^2 du
That should be ever so simple. 
Calculus 
Paul,
THanks Steve, but why 3x+5??

Calculus 
Steve,
because you have 9x^2 + 30x + 25 = (3x+5)^2