For indefinite integral, the numerator is DX and the denominator is (x square plus ax plus b)

For indefinite integral, the numerator is DX and the denominator is (x square plus ax plus b)

∫dx/（x²+ax+b）=2/√（4b-a²）arctan（（2x+a）/√（4b-a²））+C （a²＜4b）
=1/√（a²-4b）ln|（2x+a-√（a²-4b））/（2x+a+√（a²-4b）|+C （a²＞4b）

The numerator of indefinite integral is x ^ 3 and the denominator is 9 + x ^ 2
help...hepl
Indefinite integral numerator is x ^ 3 numerator and denominator is 9 + x ^ 2.

Original = ∫ (9 / X & # 179; + 1 / x) DX
=-9/(2x²)+ln|x|+C

How much is 11 times 11 times 11

11×11×11
=121×11
=1210+121
=1331

The integral of (SiNx) ln (TaNx)
Such as the title

9 × 38 + 9 × 62

9×38+9×62
=9×(38+62)
=9×100
=900

The line L passing through the right focus F of the ellipse x square / 9 + y square / 5 = 1 intersects the ellipse at two points AB, and the trajectory equation of the midpoint m of AB is obtained

Let the midpoint of AB be (x0, Y0), a (x1, Y1), B (X2, Y2) let the slope of AB be K, and the equation of AB be y = K (X-2), which is combined with the elliptic equation to get x ^ 2 / 9 + [K ^ 2 * (x ^ 2-4x + 4)] / 5 = 1 (5 + 9K ^ 2) x ^ 2-36k ^ 2x + 36K ^ 2-45 = 0, X1 + x2 = 36K ^ 2 / (5 + 9K ^ 2) = 2x0 @ Y1 + y2 = K (x1 + x2) - 4K = - 20K / (5 +

2X-4 / 3 minus 3x + 1 / 6 = x-3 / 2

Double six on both sides
2(2x-4)-(3x+1)=3(x-3)
4x-8-3x-1=3x-9
3x+3x-4x=-8-1+9
2x=0
x=0÷2
x=0

It is known that the quadratic equation 2x2 + 4x + k-1 = 0 has real roots
It is known that the quadratic equation 2x ^ 2 + 4x + k-1 = 0 has real roots and K is a positive integer
Only (3) short
(1) Find the value of K;
(2) When the equation has two non-zero integer roots, the image of the quadratic function y = 2x ^ 2 + 4x + k-1 about X is translated down 8 units, and the analytic expression of the translated function is obtained;
(3) Under the condition of (2), the image of the translated quadratic function below the x-axis is folded along the x-axis, and the rest of the image remains unchanged to get a new image. Try to explore whether the new image intersects with the line y = 1 / 2x + B? If there are several intersections?
Third, there is no B

Under the condition of (2), if the quadratic function is y = 2x ^ 2 + 4x + 2, and the image y = 2x ^ 2 + 4x + 2 is translated 8 units downward, the analytic expression of the image is y = 2x ^ 2 + 4x-6; if the image of the quadratic function y = 2x ^ 2 + 4x-6 intersects with the X axis at two points a and B, then a (- 3,0), B (1,0) when the line y = 1 / 2x + B passes through point a

When n______ 1, the quotient of a non-zero number divided by N must be less than this number

When the divisor is not zero, divided by a number greater than 1, the quotient must be less than itself; therefore, a number not 0 divided by a decimal greater than 1, the quotient must be less than this number, that is, when n > 1, the quotient of a number not 0 divided by n must be less than this number

There is a point P in the image of curve y = 1 / 2x ^ 2, which makes the distance from P to L line x-y-1 = 0 the shortest. Find the coordinates of point P, and find the distance from point P
On the curve y = (1 / 2) x ^ 2, it is not standard

A:
Let P coordinate be (x0, x0 & # / 2)
d=|x0-x0²/2-1|/√2
=|-(x0²-2x0+2)/2|/√2
=|(x0-1)²+1|/(2√2)
When x0 = 1, D is the smallest, which is √ 2 / 4
At this time, the P coordinate is (1,1 / 2)
"And find the distance between P and L" should be the distance between P and l? Yes, it is √ 2 / 4