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How to use it?
- Integral of d{x}:
-
Integral of x^(1/3)
-
Integral of sin(x)^4
-
Integral of cos(x)^3
-
Integral of (e^(x^2))
- Limit of the function:
-
x/(x+x^2)
-
Identical expressions
- x/(x+x^ two)
- x divide by (x plus x squared )
- x divide by (x plus x to the power of two)
- x/(x+x2)
- x/x+x2
- x/(x+x²)
- x/(x+x to the power of 2)
- x/x+x^2
- x divide by (x+x^2)
- x/(x+x^2)dx
-
Similar expressions
- x/(x-x^2)
Integral of x/(x+x^2) dx
The solution
You have entered
[src]
999999
/
|
| x
| ------ dx
| 2
| x + x
|
/
1
$$\int\limits_{1}^{999999} \frac{x}{x^{2} + x}\, dx$$
Integral(x/(x + x^2), (x, 1, 999999))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x + x | /
Rewrite the integrand
/2*x + 1\
|-------|
| 2 |
x \ x + x/
------ = ---------
2 2
x + x or
/ | | x | ------ dx | 2 = | x + x | /
/
|
| 2*x + 1
| ------- dx
| 2
| x + x
|
/
-------------
2 In the integral
/
|
| 2*x + 1
| ------- dx
| 2
| x + x
|
/
-------------
2 do replacement
2 u = x + x
then
the integral =
/ | | 1 | - du | u | / log(u) ------- = ------ 2 2
do backward replacement
/
|
| 2*x + 1
| ------- dx
| 2
| x + x
| / 2\
/ log\x + x /
------------- = -----------
2 2 Solution is:
C + log(1 + x)
The answer (Indefinite)
[src]
/ | / 2\ | x log(2 + 2*x) log\x + x / log(2*x) | ------ dx = C + ------------ + ----------- - -------- | 2 2 2 2 | x + x | /
$$\int \frac{x}{x^{2} + x}\, dx = C - \frac{\log{\left(2 x \right)}}{2} + \frac{\log{\left(2 x + 2 \right)}}{2} + \frac{\log{\left(x^{2} + x \right)}}{2}$$
The graph
The answer
[src]
-log(2) + log(1000000)
$$- \log{\left(2 \right)} + \log{\left(1000000 \right)}$$
=
=
-log(2) + log(1000000)
$$- \log{\left(2 \right)} + \log{\left(1000000 \right)}$$
-log(2) + log(1000000)
Use the examples entering the upper and lower limits of integration.