Finding integral ∫ (1 / (1 + sqrt (x) + sqrt (1 + x))) DX Sqrt () means square root Provide solution steps or ideas

Finding integral ∫ (1 / (1 + sqrt (x) + sqrt (1 + x))) DX Sqrt () means square root Provide solution steps or ideas

Multiplication of numerator and denominator by 1 + sqrt (x) - sqrt (1 + x)
1/(1+sqrt(x)+sqrt(1+x))
=[1 + sqrt (x) - sqrt (1 + x)] / [2 * sqrt (x)], partial fraction, the first two terms should be integrable, right
The last term ∫ sqrt (1 + x) / 2 * sqrt (x) DX = ∫ sqrt (1 + x) d (sqrt x)
Let t = sqrt (x);
Then the above formula becomes ∫ sqrt (T ^ 2 + 1) DT, and then integral by parts. If there is a formula, a set of formulas will do

Finding integral ∫ (1 / sqrt (x (1 + x))) DX
Sqrt () means square root
Provide solution steps or ideas

√(x(1+x))＝√[(x+1/2)^2－(1/2)^2]
Applying the formula: ∫ DX / √ (x ^ 2-A ^ 2) = ln| x + √ (x ^ 2-A ^ 2) | + C, the result is
ln|x＋1/2＋√(x(1+x))|＋C

The integral of X * sqrt (2 * r * x-x * x) DX

X * (2rx-x ^ 2) ^ 1 / 2DX = 1 / 2 {(2rx-2x) (2rx-x ^ 2) ^ 1 / 2} dx-r * (2rx-x ^ 2) ^ 1 / 2DX = 1 / 2 (2rx-x ^ 2) d (2rx-x ^ 2) - R * (2rx-x ^ 2) ^ 1 / 2DX the first one is OK! Integral 1 / 2 (2rx-x ^ 2) d (2rx-x ^ 2) = 1 / 4 (2rx-x ^ 2) ^ 2 the second one: because: 2rx-x ^ 2 = - (X-R) ^ 2 + R ^ 2 = R

There are books on the shelf
Hurry, hurry

There are all kinds of books on the full bookshelf

How many days is 8760 hours?

=8760 / 24 = 365 days

Calculation: 1 * 1 / 3 minus 3 * 1 / 5 Minus one in 2005 * 2007

Because 1 / [n (n + 2)] = (1 / 2) × [1 / n-1 / (n + 2)]
1/(1×3)+1/(3×5)+1/(5×7)+...+1/(2003×2005)+1/(2005×2007)
=(1/2)×(1/1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+...+(1/2)×(1/2003-1/2005)+(1/2)×(1/2005-1/2007)
=(1/2)×(1-1/3+1/3-1/5+1/5-1/5+...+1/2003-1/2005+1/2005-1/2007)
=(1/2)×(1-1/2007)
=(1/2)×2006/2007
=1003/2007
I hope I can help you. If you have any questions, please ask. I wish you progress!

Xiaogang is 180cm tall, Xiaoming is 5 / 6 of Xiaogang's, Xiaoqiang is 4 / 5 of Xiaoming's, how tall is Xiaoqiang?

180x5 / 6x4 / 5 = 120cm

English translation
five million and six hundred thousand
five hundred thousand
eighty-two million five hundred and fifty thousand
two million and one hundred thousand
twenty million thirty thousand and forty

Five million and six hundred thousand or five point six million.Five hundred thousand.Eighty -two million and five hundred fifty thousand.Two million and one hundred thousand.Twenty million thirty thou...

A skier with a mass of 60kg, each skis under his feet is 2m long, 0.1M wide and 10N heavy. The pressure on the horizontal snow surface when the skier stands on the horizontal snow surface is calculated. G = 10N / kg

When the athletes stand, the pressure on the horizontal snow surface: F = g athletes + 2G skis = m athletes G + 2G skis = 60kg × 10N / kg + 2 × 10N = 620n, the area of each skis: S1 = 2m × 0.1M = 0.2m2, the force area when the athletes stand on the horizontal snow surface: S = 2S1 = 2 × 0.2m2 = 0.4m2, the horizontal snow surface is affected by

In a square water tank with 20 sides full of water, there is a rectangular iron block 16 cm long and 10 cm wide
When the iron block is taken out, the water in the water tank drops by 2 cm. What's the height of the iron block? I want to calculate

The volume of iron is 20 × 20 × 2 = 800 cubic centimeter
The height of the iron block is 800 (16 × 10) = 5cm
A: the height of this piece of iron is 5cm