Seeking indefinite integral of the sixth power of X / (1 + X & # 178;)

Seeking indefinite integral of the sixth power of X / (1 + X & # 178;)

X ^ 6 / (1 + X & # 178;) = (x ^ 6 + 1) / (1 + X & # 178;) - 1 / (1 + X & # 178;) = (X & # 178; + 1) (x ^ 4-x & # 178; + 1) / (1 + X & # 178;) - 1 / (1 + X & # 178;) = x ^ 4-x & # 178; + 1-1 / (1 + X & # 178;) = x ^ 5 / 5-x & # 179; / 3 + x-arctanx + C

It is known that the nonzero vectors E1 and E2 are not collinear. To make Ke1 + E2 and E1 + Ke2 collinear, try to determine the value of the real number K
The process and the way to solve the problem are needed

To be collinear, let Ke1 + E2 = m (E1 + Ke2) m ≠ 0
So Ke1 + E2 = ME1 + kme2
That is, (K-M) e1 = (KM-1) E2
Because E1 and E2 are not collinear,
So K-M = 0; KM-1 = 0;
If we solve this system of equations, we get k = 1 or - 1

5 out of 6 minus 5 out of 8 equals 5 out of 8. Do it in the way of grade 5. Thank you

Let's divide 20 out of 24 times x minus 15 out of 24 = 15 out of 24
20x of 24 = 30 of 24
The solution is x = 1.5

Solution equation: 3 (X-2) = 5x (X-2)

5x (X-2) - 3 (X-2) = 0 (X-2) (5x-3) = 0  X-2 = 0 or 5x-3 = 0, ｜ X1 = 2, X2 = 35

Given the function y = log a (x2 + 2x + k), where (a > 0, a ≠ 0), if the domain of definition is r, find the value range of K

X2 + 2x + k > 0 is constant on R
Then k > - x2-2x > = 1
So the value range of K is (1, positive infinity)

Digital circuit problem: how to judge whether an asynchronous circuit composed of several JK flip flops is an addition counter or a subtraction counter?
By observing its time sequence waveform

Just now, if the front trigger q is connected to the CP end of the back trigger, at this time, when CP changes along the rising edge, it is subtraction, and CP changes along the falling edge, it is addition

It is known that one root of the equation x2 + BX + a = 0 about X is - A (a ≠ 0), then the value of A-B is ()
A. -1B. 0C. 1D. 2

∵ one root of the equation x2 + BX + a = 0 about X is - A (a ≠ 0), ∵ x1 · (- a) = a, that is, X1 = - 1, ∵ 1-B + a = 0, ∵ A-B = - 1

On the maximum coefficient of binomial expansion
Why is it necessary to compare the size of two adjacent expansion coefficients when seeking the maximum expansion coefficient? Although binomial coefficient increases first and then decreases, expansion coefficient does not necessarily increase first and then decreases?

The expansion of binomial is based on that formula. The coefficient of each term is the expansion coefficient, that is, the binomial coefficient. The numerator and denominator of CM, n are all changing. They become larger above and smaller below. Therefore, when selecting the maximum value, we must compare the coefficients of two adjacent terms. If the coefficient is greater than the former and the latter, it must be

If a + B = 5 and ab = 6, then a-b=
The standard answer is ± 1, I only calculate 1. How to calculate - 1

Because a + B = 5, the square of (a + b) is a + 2Ab + B = 25; because AB = 6, 2Ab = 12; then a + B = 13, a-2ab + B = 1, that is, the square of (a-b) is 1, so A-B = ± 1
A positive number has two square roots

In the triangle ABC, the linear equation of the height on the BC side is x-2y + 1 = 0, and the linear equation of the bisector of angle a is y = 0 if the coordinates of point B are (1,2)
Finding the linear equation of AC and BC

The equation of the bisector line of ∠ A is y = 0, which means that a is on the x-axis. Let the equation of the line where the height of a (a, 0) BC is x-2y + 1 = 0, which means that a is on the line x-2y + 1 = 0, so A-0 + 1 = 0, a = - 1, so the coordinate of a is (- 1,0). The slope of AB (2-0) / (1 + 1) = 1, because the equation of the bisector line of ∠ A is y = 0