∫7xe2x /(1 + 2x)2 dx

∫7xe2x /(1 + 2x)2 dx

∫ [xe^(2x)]/(1 + 2x)² dx
=(- 1 / 2) ∫ Xe ^ (2x) d [1 / (1 + 2x)], 1 / (1 + 2x) & # 178; integral
=(- 1 / 2) Xe ^ (2x) / (1 + 2x) + (1 / 2) ∫ 1 / (1 + 2x) d [Xe ^ (2x)]
=(- 1 / 2) Xe ^ (2x) / (1 + 2x) + (1 / 2) ∫ 1 / (1 + 2x) * e ^ (2x) * (1 + 2x) DX
= (-1/2) xe^(2x)/(1 + 2x) + (1/2)∫ e^(2x) dx
= (-1/2) xe^(2x)/(1 + 2x) + (1/4)e^(2x) + C
= e^(2x)/[4(1 + 2x)] + C
So the original formula = 7e ^ (2x) / [4 (1 + 2x)] + C

How to solve the differential equation D / dt (DX / DT) = - ω 2x of simple harmonic motion,
Omega 2 is the square of Omega

Note that x = x (T) is a function of T, which can be reduced to X '' (T) + ω & sup2; X (T) = 0. This is a second order linear equation with constant coefficients. We can first solve the characteristic equation λ & sup2; + ω & sup2; = 0 to get λ = ω I or λ = - ω I, where I is an imaginary unit, so the solution of the equation is x (T) = C1 * cos ω

What are the basic units of the international system of units? What are the international units?

There are seven basic units in the international system of units
Meter, kilogram, second, ampere, Kelvin, candela, Moore
There are many international units, not listed

Under the action of constant force F = 6N, an acceleration of 2m / S2 is generated for one object; under the action of constant force, an acceleration of 3m / S2 is generated for another object. If the constant force is applied to the third object whose mass is equal to the sum of the masses of the above two objects, the acceleration is ()
A. 1 m/s2B. 1.2m/s2C. 5 m/s2D. 6 m/s2

According to Newton's second law, there is a pair of M1, f = m1a1 ① For M2, f = m2a2 ② For M1 + m2, f = (M1 + m2) a ③ The solution is a = a1a2a1 + A2, and the data solution is a = 1.2m/s2. Therefore, B is correct, and a, C and D are wrong. Therefore, B is selected

How many hectares is an acre

One hectare is equal to 10000 square meters, and one mu is equal to 666.67 square meters
So 1 mu is equal to 0.0667 ha

1. When a stone is weighed in the air, the indication of the spring scale is 24.5 n. when it is immersed in water, the indication of the spring scale is 14.7 n. then: ① the density of the stone is

F floating = G-F indication = 24.5-14.7 = 9.8N
F = ρ liquid GV
So v = f floating / ρ liquid g = 9.8 / 1000x9.8 = 0.001 cubic meter
Mass m = g / g = 24.5 / 9.8 = 2.5kg
Object density ρ = m / v = 2.5 / 0.001 = 2500 kg / m3

The image of quadratic function passes through points a (0, - 3), B (2, - 3), C (- 1,0), 1 to find the quadratic function relation
2 find the vertex coordinates of the quadratic function image
How many units can the image of quadratic function be translated at least along the coordinate direction to make the vertex of the image at the origin

1. Let the function be
y=ax^2+bx+c
Substituting (0, - 3), (2, - 3), (- 1,0)
The solution is a = 1, B = - 2, C = - 3
So y = x ^ 2-2x-3
2. When y = 0, the solution is X1 = - 1, X2 = 3, that is, the intersection point with X axis is (- 1.0) and (3.0)
So the vertex x coordinate is (- 1 + 3) / 2 = 1
Substituting y = - 4
So vertex coordinates (1. - 4)
3. Because the vertex is (1. - 4)
Then translate 1 unit to the left along the x-axis and 4 units to the top along the y-axis, with the vertex at the origin

A container contains 100 kg pure alcohol, pour out 10 kg, add 10 kg to 15 kg, add 15 kg, pour out 20 kg, add 20 kg

1×90％×85％×80％=61.2％
As long as we grasp the change of the amount of alcohol, because the total mass remains unchanged, the first time it is reduced to 90%, water accounts for 10%, and then the alcohol and water are taken away by 15% respectively
Only the quantitative change of alcohol (1-10%) (1-15%) (1-20%) was considered

What is the law of subtraction, multiplication, division?

Subtraction:
If you subtract a positive number, use the subtracted (minus sign removed) + subtracted, and then add the minus sign
If you subtract a negative number, use the subtracted (minus sign removed) - subtract it, and then add the minus sign
Multiplication:
Negative number × negative number, directly remove the negative sign multiplication
When a positive number is multiplied by a negative number, the negative sign is added
Division:
If only one of the divisor and the divisor is negative, add a negative sign to the quotient. If both are negative, the quotient does not need to change

As shown in the figure, AB and CD are 1 / 4 arc-shaped smooth orbits with radius of R = 1m, BC is a horizontal orbit with length of 2m. An object with a mass of 2kg is released from the a-end of the orbit at rest. If the dynamic friction coefficient between the object and the horizontal orbit BC is 0.1, try to find: (1) the maximum height of the object that can rise along the CD arc-shaped orbit for the first time. (2) the distance between the object's final stop position and point B. (3) as shown in the figure If the mass of the object is 4 kg, the distance between the object's final stop position and B point

(1) Let the maximum height of the object sliding upward along the CD arc be h, then the process can be obtained by the kinetic energy theorem: Mg (R-H) - μ mgxbc = 0-0, and the solution is h = 0.8m; (2) let the total distance of the object sliding on BC be s, then the whole process from sliding to rest can be obtained by the kinetic energy theorem: Mgr - μ MGS = 0-0, and the solution is s = 10m