Gx integrate u22 u22du find gx between the limits 2x to 3x

G(x) = integrate (u^2-2) /(u^2+2)du find g(x) between the limits 2x to 3x=

We do such ;problems like this....

Take just the upper limit and plug it in :

((3x)^2 - 2) / ((3x)^2 + 2)) * d/dx(3x)

((9x^2 - 2) / (9x^2 + 2)) * 3

Combining :

(27x^2 - 6) / (9x^2 + 2) --> ONE

Now, do the same for the lower limit :

((2x)^2 -2) / ((2x)^2 + 2)) * d/dx(2x)

((4x^2 - 2) / (4x^2 + 2)) * 2

(2x^2 - 1) / (2x^2 + 1) * 2

(4x^2 - 2) / (2x^2 + 1) ---> TWO

Now, we simply subtract ONE and TWO :

(27x^2 - 6) / (9x^2 + 2) - (4x^2 - 2) / (2x^2 + 1)

Now, we can combine this using common denominatoe method :

(18x^4 + 25x^2 - 2) / ((2x^2 + 1)(9x^2 + 2)) ---> ANSWER