1 / (x ^ 2-A ^ 2) indefinite integral The results show that (1 / 2a) ln | (x - a) / (x + a) | + C has absolute value But why is the derivative of this result different from 1 / (x ^ 2-A ^ 2), with a negative sign in front of it

1 / (x ^ 2-A ^ 2) indefinite integral The results show that (1 / 2a) ln | (x - a) / (x + a) | + C has absolute value But why is the derivative of this result different from 1 / (x ^ 2-A ^ 2), with a negative sign in front of it

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Seeking indefinite integral of X / (x + 1) (x + 2) (x + 3)

1/(x+1)(x+2)(x+3)=1/(x+1)[1/(x+2)-1/(x+3)]
=1/[(x+1)(x+2)]-1/[(x+1)(x+3)]
=1/(x+1)-1/(x+2)-1/2[1/(x+1)-1/(x+3)]
=1/[2(x+1)]-1/(x+2)+1/[2(x+3)]
∫x/(x+a)dx=∫[1-a/(x+a)]dx=x-aln|x+a|+C
∫x/(x+1)(x+2)(x+3)dx
=∫x/[2(x+1)]-x/(x+2)-x/[2(x+3)]dx
=1/2∫x/(x+1)dx-∫x/(x+2)dx+1/2∫x/(x+3)dx
=1/2(x-ln|x+1|)-(x-2ln|x+2|)+1/2(x-3ln|x+3|)+C
=-1/2ln|x+1|+2ln|x+2|-3/2ln|x+3|+C

The original function of indefinite integral 1 / [(x + 1) (x ^ 2 + 1) ^ (1 / 2)]

Let x = tank
Then DX = sec ^ 2 TDT
The formula is: ∫ 1 / [(tant + 1) sect] * sec ^ 2 T DT = ∫ DT / (Sint + cost) = √ 2 ∫ DT / sin (T + π / 4)
By ∫ Du / sinu = sinudu / (sinu) ^ 2 = - ∫ D (COSU) / (1-cos ^ 2U) = - 0.5 ∫ D (COSU) * [1 / (1-cosu) + 1 / (1 + COSU)] = - 0.5 [- ln (1-cosu) + ln (1 + COSU)] = - 0.5ln [(1 + COSU) / (1-cosu)] = - 0.5ln (1 + COSU) ^ 2 / (sinu) ^ 2 = ln | sinu | / (1 + COSU)] = - 0.5ln [(1 + COSU) / (1 + COSU)] = - 0.5ln (1 + COSU) ^ 2 = ln | sinu | / (1 + COSU)
Therefore, the original formula = √ 2ln | sin (T + π / 4) | / (1 + cos (T + π / 4) + C is obtained by substituting t

What is 123456789 times 2

246913578

The downwind transport team shipped 10000 porcelain bowls, with the freight of 0.15 yuan per bowl. If one bowl was damaged, it would not only not pay the freight, but also compensate 2 yuan. After completing the task, the team got a total freight of 1465.6 yuan. How many bowls were damaged in the transport?

Set X damaged
0.15*(10000-X)-2X=1465.6
1500-2.15X=1465.6
2.15X=34.4
X=16
16 damaged

The meaning of 3.7 × 0.8 is______ The product of 5.6 times two decimal places is______ Decimals

According to the meaning of decimal multiplication, we can get: (1) the meaning of 3.7 × 0.8 is: what is 8 / 10 of 3.7; (2) 5.6 times two decimal places, when the percentile of the two decimal places is not 5, the decimal places of their product are: 1 + 2 = 3 (places); when the two decimal places are 0.25, 5.6 × 0.25 = 1.4, it

1583.45 how to use scientific notation (keep three significant digits)
How did you get the answer?

3 times of 1.58 * 10
Keep three significant digits, three digits from left to right, expressed by a few points, and then multiplied by several power

How to write the first composition in the first volume of the fifth grade Chinese book of the people's education press

I grew up in reading
I've loved reading since I was a child. In the bright sunshine, I spread a book on my knee, smelling the faint fragrance of ink on the thin paper, and put a glass of water beside me to listen to the wonderful sound of the wind blowing the pages. In order to edify my character of reading, my mother installed a red bookshelf on the wall of my home. I always stood in front and looked up at those colorful brochures, I know that my love for books has been deeply imprinted in my heart since then
The book has made me understand the vast world and infinite knowledge, but the book called "try again" has the most profound influence on me. My mathematics has always been poor. No matter how hard I listen to the teacher and work hard, my score is always around 80 points. After several tests, my score has not changed much, I was a little frustrated and wanted to give up my efforts. My mother didn't say much when I saw that I didn't want to forge ahead and wanted to fall back. Just on my birthday, she gave me a book called try again. It's a humble book with a light blue cover. It's elegant and ordinary. It's about a college student who worked hard in business after graduation, The plot is not fashionable, or even a bit conventional, but there is a sentence that impresses me deeply: "when you fail many times, don't give up, because if you lose the belief of success at this time, the previous failure will be wasted. Every failure is a test of success for you. If you fail more than once, you will be further away from success, Try again, maybe you will succeed. "This book tells me two short sentences, but it is also a truth that has far-reaching influence on me. I understand my mother's good intentions. In the future study, whenever I am sad and depressed after failure, I will think of this" try again ". I always say to myself" try again, I will succeed ". Finally, My math scores jumped to the top of the class. In the face of my progress, I laughed, my mother laughed, I think the book, also laughed
In fact, I really should thank the book, the book not only gave me a lot of tangible knowledge, but also injected me with a lot of intangible power, taught me a lot of profound truth, pointed out the direction for my life voyage

As shown in the figure, it is known that the function expression of the straight line L is y = - 43x + 8, and l intersects with the X axis and Y axis at two points a and B respectively. The moving point Q starts from point B and moves to point a at a speed of 2 units per second on the line Ba, while the moving point P starts from point a and moves to point o at a speed of 1 unit per second on the line Ao. Set the moving time of points Q and P as T seconds. (1) calculate the coordinates of points a and B. (2) when t is the value, Are triangles with vertices a, P and Q similar to △ AOB? (3) The length of line segment PQ in (2) is obtained when the triangle with vertices a, P and Q is similar to △ AOB

(1) Y = - 43x + 8, when x = 0, y = 8, when y = 0, x = 6, the answer is: the coordinates of point a are: (6, 0), and the coordinates of point B are: (0, 8). (2) there are two cases of this problem: in △ ABO, ∠ boa = 90 °, OA = 6, OB = 8, according to Pythagorean theorem: ab = 10, ∵ ∠ Bao = ∠ Bao, BQ = 2T, AQ = 10 -

There are 2003 numbers on the blackboard. Erase two numbers at any time and write another one______ After that, there is only one number left on the blackboard

Wipe two at any time, write another one, reduce the number of 1, do not write the last time, so, need 2003-2 + 1-2 + 1-2 + 1 =2003-1-1 = (2003-2) / (2-1) + 1 = 2002 (Times). A: after 2002 times, there is only one number left on the blackboard