For indefinite integral DX / (3x ^ 2-1) please be more detailed, thank you

For indefinite integral DX / (3x ^ 2-1) please be more detailed, thank you

∫dx/(3x^2-1)=(1/2√3)[∫d(√3x-1)/(√3x-1)-∫d(√3x+1)/(√3x+1)]
=(1/2√3)[ln(√3x-1)-ln(√3x+1))

9.2 finding indefinite integral ∫ (x ^ 2-3x + 2) DX
nine point five

Original form
=x^3/3-3x^2/2+2x+C

Given that a = (3,2, - 2 / - K, - 1, K / 4,2, - 3), when we ask what is the value of K, there is an invertible matrix P, so that p-1ap is a diagonal matrix? Find out P and the corresponding diagonal matrix

|A - λ e | = 3 - λ 2 - 2 - K - 1 - λ K42 - 3 - λ R3 - R13 - λ 2 - 2 - K - 1 - λ K1 + λ 0 - 1 - λ C1 + C31 - λ 2 - 20 - 1 - λ K00 - 1 - λ = (1 - λ) (1 + λ) ^ 2, so the eigenvalues of a are 1, - 1, - 1

50×51/1+51×52/1+52×53/1+53×54/1+54×55/1

50 × 51 / 1 + 51 × 52 / 1 + 52 × 53 / 1 + 53 × 54 / 1 + 54 × 55 / 1 Analysis: 50 × 51 / 1 = (51-50) / 50 × 51 = 1 / 50-1 / 51 × 52 / 1 = (52-51) / 51 × 52 = 1 / 51-1 / 52 × 53 / 1 = (53-52) / 52 × 53 = 1 / 52-1 / 53 × 54 / 1 = (54-53) / 53

If (x + 1) & #179; = 0.008, then x = if (x + 1) & #178; = 0.04, then x=

（x+1）³=0.008=8/1000=2³/10³=(2/10)³=1/5 ³x+1=1/5x= - 4/5（x+1）²=0.04=4/100=2²/10²=(2/10)²=1/5²x+1=1/5x= - 4/5

11 out of 12 + 15 out of 16 + 8 out of 15 =? 7 out of 12 + 5 out of 32 + 9 out of 48 =?
Please simplify the calculation or reduce it to a fraction

The first answer is 191 / 80, and the second is 13 / 32

Factorization: ab (a-b) 2-a2b (B-A)

ab（a-b）2-a2b（b-a）=ab（b-a）2-a2b（b-a）=ab（b-a）[（b-a）-a]=ab（b-a）（b-2a）．

(- 5) times minus 3 / 7 6 plus (- 7) times (- 3 / 7 6) minus (- 12) times (- 3 / 7 6)
There is another [1 and 2 / 3 minus (1 / 3 minus 1 / 6 plus 5 / 12) times 2.4] times 5

(- 5) times minus 3 / 7 6 plus (- 7) times (- 3 / 7 6) minus (- 12) times (- 3 / 7 6)
=6X (5 + 7-12)
=6x0 3 / 7
=0
[1 and 2 / 3 minus (1 / 3 minus 1 / 6 plus 5 / 12) times 2.4] times 5
=5/3x5-(1/3-1/6+5/12)x12
=25/3-1/3x12+1/6x12-5/12x12
=25/3-4+2-5
=4/3

A 3-meter-long wood is sawed into 3 sections, and the surface area is increased by 18 square decimeters. What is the original volume of this wood?

3 meters = 30 decimeters, 18 △ 4 (3 + 1) = 18 △ 4, = 4.5 (square decimeters); 4.5 × 30 = 135 (cubic decimeters); answer: the original volume of this wood is 135 cubic decimeters

A six digit number is 23x56x, which is a multiple of 88. What is the quotient of this number divided by 88

88 has factors 11 and 8. If 23 Χ 56x is a multiple of 88, 23 Χ 56x must be a multiple of 11 and 8. The characteristic of the multiple of 11 is that the difference between odd digit and even digit can be divisible by 11, that is, (x + 5 + 3) - (6 + X + 2) = 0 or (6 + X + 2) - (x + 5 + 3) = 00 △ 11 = 0