Evaluate the following definite integral:

Question

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

Answer 1

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.

Answer 2

THanks Steve, but why 3x+5??

Answer 3

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