How to calculate the indefinite integral of 1 / (x ^ 2-A ^ 2) ^ (3 / 2)?

∫dx/(x²-a²)^(3/2)
Let x = asecu, DX = asecutinu Du
The original formula = a ∫ secutanu / (A & sup2; sec & sup2; U-A & sup2;) ^ (3 / 2) Du
=a∫secutanu/(a²tan²u)^(3/2) du
=a∫secutanu/(a³tan³u) du
=1/a²*∫secu/tan²u du
=1/a²*∫cscucotu du
=1 / A & sup2; * (- CSC & sup2; U) + C, draw an auxiliary triangle to be solvable, such that the hypotenuse = x, the adjacent side = a, the opposite side = √ (X & sup2; - A & sup2;)
=-x/[a²√(x²-a²)]+C

How to find 1 / (x ^ 2 + A ^ 2) ^ 3 / 2 indefinite integral

x=atanu
dx=asec^2udu
The original formula = ∫ cosudu / A ^ 2
=sinu/a^2+C
=x/(a^2√a^2+x^2)+C

How to find the indefinite integral of 1 / 2 (x-a ^ 2)
By the way, I'd like to ask you about the indefinite integral of (x + 3) X. I've confused all these methods. I hope children's shoes can help me. And when will the above method of (x + a) - (x-a) be used?

Let u = u = x-a and\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\8747; (secptanp) / A & # 178; Tan & # 178; P DP = (...)

Solution equation: 3x-8 / 15 = 7 / 15

3x-8/15=7/15
3x=7/15+8/15
3x=1
x=1/3

How to calculate 125 * 88 simply

125*88=125*（80+8）=125*80+125*8=10000+1000=11000

As shown in the figure, an isosceles trapezoid flowerbed is designed. The upper bottom of the flowerbed is 100m long, the lower bottom is 180m long, and the distance between the upper and lower bottom is 80m. There is a transverse corridor outside the middle line of the two waist, and there are two longitudinal corridors between the upper and lower bottom. The width of each corridor is equal, and the area of the corridor is one sixth of the trapezoid area. What is the width of the corridor (accurate to 0.01M)? (friendly tip: the median line of the middle corridor is the median line of the isosceles trapezoid)

Let the width of the corridor be XM. According to the meaning of the title, we can get 100 + 1802x + 2x × 80-2x2 = 16 × 100 + 1802 × 80. After sorting out, we can get 3x2-450x + 2800 = 0, ｜ X1 = 225 + 516893 ＞ 80 (rounding off), X2 = 225 − 516893 ≈ 6.50 A: the width of the corridor is about 6.50m

If you want to reduce the price by 35% first and then by 20% after the reduction, the current price is ()% of the original price

For one, the price should be reduced by 35% first, and then by 20% according to the price after the reduction, then the current price is (52%) of the price before the reduction
(1-35%)×（1-20%）=52%

It is known that the domain of definition of function y = f (x) is r, and for any a, B ∈ R, f (a + b) = f (a) + F (b). When x > 0, f (x) < 0 holds, f (3) = - 3. (1) prove that function y = f (x) is a decreasing function on R; (2) prove that function y = f (x) is an odd function; (3) try to find the range of function y = f (x) on [M, n] (m, n ∈ n *)

It is proved that: (1) let x1 ＞ X2, then x1-x2 ＞ 0, f (x1-x2) ＜ 0, and f (a + b) = f (a) + F (b), f (x1) = f (x1-x2 + x2) = f (x1-x2) + F (x2) ＜ f (x2) ｜ function y = f (x) is a decreasing function on R; (2) it is proved that f (x-x) = f (x) + F (- x) from F (a + b) = f (a) + F (b), that is, f (x) + F (- x) = f (0), and f (0) = f (0) from a = b = 0 (- x) = - f (x), that is, the function y = f (x) is an odd function, (3) by the function y = f (x) is a monotone decreasing function on R, y = f (x) is also a monotone decreasing function on [M, n]. The maximum value of y = f (x) on [M, n] is f (m), and the minimum value is f (n).. f (n) = f [1 + (n-1)] = f (1) + F (n-1) = 2F (1) + F (n-2) ∧ NF (1). Similarly, f (m) = MF (1) ∧ Therefore, the range of function y = f (x) on [M, n] is [- N, - M]

Known sequence an = 2n + 1 design algorithm output first 100 items

It's an arithmetic sequence
The general formula of arithmetic sequence {an} is an = 2n + 1
a1=3
Its first n terms and Sn = n (a1 + an) / 2 = n (3 + 2n + 1) / 2 = n (n + 2)
You can count it in~

How to calculate the indefinite integral of 1 / (x ^ 2-A ^ 2) ^ (3 / 2)?