Who can explain how to solve this integral?

Question

The integral from 5 to 7 of (5x^2 +4)/(x^2)

Is it integration by parts or substitution? I can't figure out how to get it into a form that I can integrate.

Answer 1

start by separating the integrals, (S = Integral Sign)

S((5x^2 +4)/(x^2)) = S(5x^2 / x^2) + S(4 / x^2)

simplify to:

S(5) + S(4/x^2)

pull out constants

5S(1) + 4S(1/x^2)

integrate and solve for limits

Answer 2

Well, what i would do first is split the fraction up into:

5x^2/x^2 + 4/x^2

then take the integral separately.

[integral] 5x^2/x^2

[integral] 5

5x

[integral]4/x^2

4[integral] x^-2

-4/x

5x - 4/x + c

Then just evaluate the integral.

Hope that helps!

Answer 3

integrating by parts probably wouldn't work. you can try this:

seperate the fraction so it becomes 5 + 4/x^2. which is simpler, then all you have to do is integrate 5 +4*x^ -2, then it just becomes a regular integration