Finding the root of ∫ DX / X 1-x2 by the second kind of substitution method

Finding the root of ∫ DX / X 1-x2 by the second kind of substitution method

Let x = Sint, then DX = cost DT, √ (1-x ^ 2) = cost, so the original integral = ∫ cost / cost * 1 / Sint DT = ∫ 1 / Sint DT = ln | 1 / sint - Cott | + C, and 1 / Sint = 1 / x, Cott = cost / Sint = √ (1-x ^ 2) / x, so the original integral = ln | 1 / X - √ (1-x ^ 2) / X | + C, C is constant

Finding integral ∫ DX / (x + 2) × (x + 1) &# 189; &# 189; by the second kind of substitution method

Let t = √ (x + 1), then x = T ^ 2-1, DX = 2tdt
∫1/(x+2)√(x+1)dx
=∫2tdt/(t^2+1)t
=2∫1/(t^2+1)dt
=2arctant+C
=2arctan√(x+1) + C
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Solving indefinite integral ∫ x * √ (x ^ 2 + 3) DX by substitution method

Decomposition factor: BC (B + C) + Ca (C-A) - AB (a + b)=______ ．

bc（b+c）+ac（c-a）-ab（a+b）=c[b（b+c）+a（c-a）]-ab（a+b） =c（b2+bc+ac-a2）-ab（a+b） =c[（bc+ac）+（b2-a2）]-ab（a+b）=c[c（b+a）+（b+a）（b-a）]-ab（a+b） =c（a+b）（c+b-a）-ab（a+b） =（a+b）（c...

When the store enters a batch of clothes, it will lose 110 yuan if each piece of clothes is sold at 60% of the price, while it will gain 70 yuan if it is sold at 80% of the price. How much is the price of each piece of clothes? How much is the price of each piece of clothes? (it must be one yuan at a time.)

Set the price as X
According to the price of 60% sale will lose 110 yuan
The original price is 0.6x + 110
If sold at a 20% discount on the list price, it will earn 70 yuan
The original price is 0.8x-70
Lie equation
0.6X+110=0.8X-70
X＝900
So the original price is 650

Let a be a real symmetric matrix of order m and positive definite, and B be a m × n matrix. It is proved that btab is a positive definite matrix if and only if rankb = n

OK & nbsp; here is a picture & nbsp; please click to see the larger picture

Factorization: X & # 178; - 4 (x-1) =?

x²-4（x-1）
Original formula = x & # 178; - 4x + 4
=(x-2)²

Given that the value of fraction 6 (a + 3) / a2-9 is a positive number, find the value range of A~

Is the square of a minus 9, if so, a > 3

Let f (x) satisfy f (x) = 4x2 + 2x + 1. (1) Let G (x) = f (x-1) - 2x, find the range of G (x) on [- 2,5]; (2) let H (x) = f (x) - MX, be a monotone function on [2,4], find the range of M

(1) Because f (x) = 4x2 + 2x + 1, G (x) = f (x-1) - 2x = 4 (x-1) 2 + 2 (x-1) + 1-2x = 4x2-8x + 3, because g (x) is a quadratic function with the opening direction upward and the axis of symmetry x = 1, G (x) monotonically decreases on [- 2,1] and increases on [1,5], so its minimum value is g (...)

If K is not equal to 0, can X be equal to 0?

No, you can look at the image of the inverse scale function, and you will find that it has no intersection with the Y axis, so x = 0 is not available