How to find the original function ln (1 + x ^ 2)

How to find the original function ln (1 + x ^ 2)

∫ln(1+x^2) dx
= xln(1+x^2) - 2∫ [x^2/(1+x^2)] dx
= xln(1+x^2) - 2∫ dx + 2∫ dx/(1+x^2)
= xln(1+x^2) - 2x + 2arctanx + C

Finding the primitive function of Ln (x ^ 2 + 1)

Part by part integration method:
∫ln(x^2+1)dx
=xln(x^2+1)-∫2x^2/(x^2+1）dx
=xln(x^2+1)-2∫[1-1/(x^2+1)]dx
=xln(x^2+1)-2[x-arctanx]+C
=xln(x^2+1)-2x+2arctanx+C

The original function of F (x) = 1 (x + 1) is ln (x + 1) or ln | x + 1|
How to derive the absolute value of logarithmic function, such as ln|x + 1|

Ln | x + 1 | the verification of this formula depends on different situations. The reason why we do not take ln (x + 1) is that ln (x + 1) is meaningful to the integrand function except x = - 1, while ln (x + 1) is only meaningful to x > - 1, but in fact x is not

Car a and car B run from 798 kilometers away and meet each other in 7 hours. Car a runs 6 kilometers less than car B per hour, and car a and car B run 6 kilometers less than car B per hour
How many kilometers per hour do a and B cars travel

Car a and car B drive from 798 kilometers away and meet each other in 7 hours. Car a travels 6 kilometers less than car B per hour. How many kilometers does car a and car B travel per hour?
A (798 △ 7-6) △ 2
=（114-6）÷2
=108÷2
=54 km / h
B 54 + 6 = 60 km / h

A number consists of three 10's, five 0.1's and eight 0.001's

30.508
thirty point five zero eight

On a map with a scale of 1:5000000, the distance between a and B is 9cm. If on a map with a scale of 1:7500000, how many cm is the distance between a and B? (with scale knowledge)
Write the formula (with proportion knowledge)

Actual distance = distance on the map △ scale
So AB actual distance = 9 △ 1 / 5000000 = 45000000cm
On a 1:7500000 scale map,
Distance on the map = actual distance × scale = 45000000 × 1 / 7500000 = 6cm
(but getting something for nothing is not a good thing. I hope you can do it yourself next time.)

Mathematical master, please come in, use Cauchy inequality to find the most value
What is the maximum value of root (7-x & sup2;) + root (X & sup2; + 1)

Cauchy inequality (A2 + B2 +...) )(x2+y2+… )>=(ax+by+… )2
In the above formula, 2 is square, the font is not easy to change, sorry
[(7-x2) + (x2 + 1)] (1 + 1) > = {root (7-x & sup2;) + root (X & sup2; + 1)} 2
So the root sign (7-x & sup2;) + the root sign (X & sup2; + 1)

A ton of coal weighs five sixths of a ton. It will be burned in five days. How many tons of coal will be burned every day on average, and how many parts of this ton of coal will be burned every day
A pile of coal weighs five sixths of a ton and is burned out in five days. How many tons are burned every day on average, and what percentage of this pile of coal is burned every day?
The ratio of the degrees of the three internal angles of a triangle is 1:1: This is a () triangle with () axes of symmetry
The number of a is 72, one sixth of a is equal to one fourth of B, and the number of B is ()
25% of a number is 50, and 5% of it is ()
It takes 10 hours for Party A and 8 hours for Party B to complete the same work. The ratio of work efficiency between Party A and Party B is ()
In a shopping mall's new year's day shopping activities, the original price of 1236 yuan washing machine, 75% off, the price is ()
The supermarket brought in 180 cases of apples, two fifths more than pears. How many cases of pears?
A canteen burned 2000 kg of coal in April, 20% less than that in March. How many kg of coal was burned in March?

5 / 6 △ 5 = 1 / 6 ton
A: it burns an average of 1 / 6 ton per day
1÷5=1/5
A: one fifth of the coal is burned every day

What's the difference between inequality and inequality with absolute value!

Inequality with absolute value should be discussed in different cases when absolute value is removed
So an inequality with absolute value should be reduced to at least two inequalities without absolute value
For example: | X-5 | + 2 > 2x
It can be changed into:
（1）
X-5>0
X-5+2>2X
(2)
X-52X

Party A and Party B face each other and meet each other in 6 hours. Party A travels 60 km more than Party B. the memory speed ratio is 11:9. What's the speed of Party A?

The speed ratio is 11:9
A goes 11 / (11 + 9) = 11 / 20
B left 9 / 20
Whole course = 60 / (11 / 20-9 / 20) = 600
Closing speed = 600 / 6 = 100
A is 100 * 11 / 20 = 55