Finding the original function of Ln (x-1) times x

Finding the original function of Ln (x-1) times x

Partial integration method: ∫ XLN (x-1) DX = (x ^ 2 / 2) ln (x-1) -∫ (x ^ 2 / 2) / (x-1) DX = (x ^ 2 / 2) ln (x-1) - 1 / 2 ∫ (x ^ 2-x + X-1 + 1) / (x-1) DX = (x ^ 2 / 2) ln (x-1) - 1 / 2 ∫ [x + 1 + 1 / (x-1)] DX = (x ^ 2 / 2) ln (x-1) - 1 / 2 [x ^ 2 / 2 + X + ln | X-1] + C

Let f (x) = 1 / [(x + 1) ln (x + 1)] (x > - 1 and X not equal to 0
(1) Finding monotone interval of function f (x)
(2) Finding the range of function f (x)
(3) Given that 2 ^ 1 / x + 1 > (x + 1) ^ m is (- 1,0) constant for any x, find the value range of real number M
Don't copy from soso. If you are satisfied, add 20 points. The focus is on the second question

Let x + 1 = t (T > 0), then G (T) = tlnt
When t → + ∞, G (T) → + ∞,
G (1 / T) = ln (1 / T) / T = - LNT / T → 0, that is, G (T) → 0 when t → 0
G '(T) = 1 + LNT, G (T) is negative and decreasing on (0,1 / E) and increasing on (1 / E, + ∞), where g (T) is positive on (1, + ∞)
Therefore, f (x) increases at (0,1 / E-1), decreases at (1 / e-1,0), and decreases at (0, + ∞)
f(1/e-1)=-e
So the range of F (x) is (- ∞, - e] ∪ (0, + ∞)
(3) Take logarithm, M

Find the positive integer solution of the system of inequalities X-2 (x-3) less than or equal to 8, X / 2 - (x-3) > 1 / 4

From the first inequality, we get x > = - 2
The solution of the second inequality is X

The bus and the truck leave each other from a and B and meet in 5 hours. After meeting, the bus takes another 4 hours to arrive at B. at this time, the truck is 60 kilometers away from A. how many kilometers is the distance between a and B?

The speed ratio of the two cars is 5:4
The distance between a and B
60÷（1-4/5）
=60÷1/5
=300 km
In the top right corner of my answer, click comment, and then you can choose satisfied, the problem has been solved perfectly

Set a = {a + 2, A-1, A2 + 3A + 3}, if 1 belongs to a, find the value of real number a

1) If a + 2 = 1, then a = - 1, A-1 = - 2, A2 + 3A + 3 = 1 has the same elements, then a = - 1 does not have the same meaning. 2) if A-1 = 1, then a = 2, a + 2 = 4, A2 + 3A + 3 = 13, so a = 2 satisfies the meaning. 3) if A2 + 3A + 3 = 1, then a = - 1 or a = - 2, a = - 1

If the number of a increases by 1 / 3 and the number of B increases by 2 / 5, the two numbers are equal. What is the original number of a?
Don't use those proportions

If two numbers are equal, it is 28
A: 28 (1 + 1 / 3) = 21
B: 28 (1 + 2 / 5) = 20
The original number a is the number B: 21 / 20

How many natural numbers are there between 0 and 1000
The sum of the numbers in each digit of is equal to 15

In fact, we investigate permutation and combination, decompose 15 = 6 + 9 = 7 + 8, and get a (2,2) + a (2,2) = 4. Decompose it into the sum of three different numbers, 15 = 1 + 5 + 9 = 1 + 6 + 8 = 2 + 4 + 9 = 2 + 5 + 8 = 2 + 6 + 7 = 3 + 4 + 8 = 3 + 5 + 7 = 4 + 5 + 6, and get the combination of different numbers as 8 × a (3,3) = 48, decompose it into two identical numbers, 15 = 3 + 3 + 9 = 4 +

Car a and car B have the same speed from city a to city B. car a starts 120 kilometers before car B starts. Car a returns immediately after arriving at city B, five minutes away from city B
One met car B and asked: how many kilometers are there between city a and city B? Why should 120 be divided by 2

I'm sorry, I went back last night, I didn't answer for you in time
I don't know how to write your answer. If you need to explain the reason of your answer, ask me your answer
Now I'll use the equation method to solve it for you
Let a and B be x kilometers apart, then a goes at the same time: x-120 + 1 / 5x kilometers, and B goes at (1-1 / 5) x kilometers
x-120+1/5x=(1-1/5)x
6/5*x-120=4/5*x
6/5*x-4/5*x=120
2/5*x=120
x=120*5/2
x=300
A: A and B are 300 kilometers apart

1. The sum of the internal angles of a triangle is 180 ° () 2. The sum of the degrees of the four internal angles of a parallelogram is 360 ° ()
1. The sum of the internal angles of a triangle is 180 degrees
2. The sum of the degrees of the four internal angles of a parallelogram is 360 degrees
3. Equations with unknowns are called equations
4. When a = 2, the square of a = 2A
5.1.5b+0.5b=2b.（ ）
Equation of 6.8x + 12 < 100 ()
The solution of 7. X - 2. 5 = 7. 5 is the equation
8. Circular decimals are infinite

1 to 2 to 3 wrong 4 to 5 to 6 wrong 7 to 8 right

People's Park is the starting point of No.1 and No.3 buses. No.1 bus No.3 will be distributed once, No.3 bus No.5 will be distributed once. After these two buses start at the same time, they will be distributed at least a few minutes later
This is a math problem. Thank you for your answer. There is another problem: cut a rectangular piece of paper 60 cm in length and 45 cm in width into a square of the same size. There is no surplus. The square should be as large as possible. How many centimeters is the side length of the cut Square? How many pieces can it be cut into?

641904632,
People's Park is the starting point of No.1 and No.3 buses. No.1 bus No.3 will be distributed once, No.3 bus No.5 will be distributed once. After these two buses start at the same time, how many minutes will they start at the same time?
3 × 5 = 15 (min)
Cut a 60cm long and 45cm wide rectangular piece of paper into a square of the same size
How many centimeters is the side length of the cut square?
The greatest common factor of 60 and 45 is 15, so the continuous length of a square is 15 cm
How many can be cut into?
(60 / 15) × (45 / 15) = 12