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