Question 1

Here I will simply find a primitive function

int 1 / (x ^ 2-4x +4) (x ^ 2-4x +5) dx

Trying to simplify and go with the first brackets, get it to (x-2) ^ 2 Thus, I write it as

int 1 / (x-2) ^ 2 (x ^ 2-4x +5) dx

Then I used partialbråksuppdelning, this makes me a bit confused about whether I was right or if it is particularly clever, given the results further ahead.

A / (x-2) + B / (x-2) ^ 2 + (CX + D) / (x ^ 2-4x +5)

Then you should get all the same denominator and then multiplying the terms. But since I only had a 1 from the beginning in the numeratorthen there isare no CX , thenC = 0

(A (x ^ 2-4x +5) (x 2) + B (x ^ 2-4x +5) + (CX + D) (x-2) ^ 2) / ((x-2) ^ 2 * (x ^ 2-4x + 5))

Multiplies simply set my A, B, CX, but not sure if I right, or what the problem actually becomes

x ^ 3 (A + C) = 0

x ^ 2 (-6A + B-4C + D) = 0

X (13A-4B +4 C-4D) = 0

1 (-10A + 5B +4 D) = 1

Then I'll do the Gaussian elimination and concludes

C = 0

B = -1

D = - 1 / 12

A = - 1 / 3

I put in these values in the original approach with partialbråksuppdelning so it will hardly be of any use?

Only the first term is easy to do primitive functions to, the other two are just as difficult as before ..

Question 2A barrel emits water with 0.52te ^ (-0.89t) cm ^ 3/day when it emits at most per day and how much is it?

I perceive it as a derivative, it is a rate because it is cm ^ 3/day and want to look up function to find out how much it is. int = integral

int 0.52te ^ (-089t) dt

Do partial integration chooses t g, e, f and move out beyond 0.52 int

0.52 int t * e ^ (-0.89t) dt = [(e ^-0.89t) * t / (-0.89) * t] - int 1 * e ^-0.89t

What goes up must come up with intergralen to the last and it is simple it is (e ^ -0.89 t) / (-0.89)

Thus, the function will

f (t) = 0:52 * ((e ^ -0.89 t) * t / (-0.89) e ^ -0.89 t / (-0.89))

Finds zero, put the = 0 and you get a zero, which is

t = 1

Then do I simply set the value of the primitive function .. but it feels wrong? How am I going to anyway?