What's the integral of LNX?

What's the integral of LNX?

Xlnx-x + C, integral by parts~

Calculation: (1) 22 + (4-7) △ 32 + (- 1) 2007; (2) 6x - (2x-y) - [2Y + (x-3y)]

(1) Original formula = 4 + (- 3) × 23 + (- 1) = 4-2-1 = 1 (2) original formula = 6x-2x + y-2y-x + 3Y = 3x + 2Y

Given that the constant term in the expansion of (AX-1 / √ x) ^ 6 (a > 0) is 60, then the coefficient of x ^ 2 in the expansion of (x + a) (x-1) ^ 4 is 60

In the expansion of (AX-1 / √ x) ^ 6, t = C (6, R) (AX) ^ (6-r) * (- 1 / √ x) ^ R = (- 1) ^ R * a ^ (6-r) * C (6, R) * x ^ (6-3r / 2), 6-3r / 2 = 0, r = 4, ｜ constant term = T5 = a ^ 2 * C (6,4) = 15A ^ 2 = 60, a ^ 2 = 4, a > 0, ｜ a = 2 +6X ^ 2-4x + 1)

Calculate (2 × 10 ^ - 5) ^ 3 ^ (3 × 10 ^ - 4) ^ - 2

(2×10^-5)^3÷(3×10^-4)^-2
=【2^3×10^-15】÷【3^-2×10^8】
=8*10^-15÷【1/9×10^8】
=8*10^-15 *9×10^8
=72*10^(-15+8)
=72*10^-7
=7.2*10^-6

Let constant a > 0, the coefficient of coefficient X ^ 3 in (AX ^ 2 + 1 / √ x) ^ 4 expansion is 3 / 2, a =?
rt

a = 1/2

Calculation: (2 × 10 ^ - 5) ^ 2 ^ (3 × 10 ^ - 2) ^ - 2

(2*10^-5)^2/(3*10^-2)^-2
2^2*10^(-10)/3^(-2)*10^4

LIM (x ^ 3 + KX ^ 2 + 3x-2) / x ^ 2-1 = 0, then K

Because LIM (x ^ 3 + KX ^ 2 + 3x-2) / x ^ 2-1 = 0, x ^ 2-1 = (x-1) (x + 1)
So the value of X is plus or minus 1
We can know by substitution
K = 6 or - 2

1×2+2×3+3×4+… +How about 10 × 11

1*2+2*3+3*4+4*5+5*6+6*7+7*8+8*9+9*10+10*11 ````=1+1+2+2+3+3+4+4+5+5+6+6+7+7+8+8+9+9+10+10 ```=1+2+3+4+5+6+7+8+9+10+1+2+3+4+5+6+7+8+9+10 ```=10(10+1)(2*10+1)/6+10(1+10)/2 ```=385+55 ```=440

LIM (x ^ 6 + x ^ 5) ^ (1 / 6) - (x ^ 6-x ^ 5) ^ (1 / 6) x approaches infinity

Calculate 1 / 2 * 1 / 3 + 1 / 3 * 1 / 4 + 1 / 4 * 1 / 5 + 1 / 5 * 1 / 6 +. + 1 / 10 * 1 / 11

1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+.+1/10*1/11
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.+1/10-1/11
=1/2-1/11
=9/22