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-
How to use it?
- Integral of d{x}:
-
Integral of e^(3*x)
-
Integral of x*exp(x)
- Integral of sin(ln(x))/x
-
Integral of e^(x*(-2))
- Graphing y =:
- x/(x^2+2)
- Derivative of:
-
x/(x^2+2)
-
Identical expressions
- x/(x^ two + two)
- x divide by (x squared plus 2)
- x divide by (x to the power of two plus two)
- x/(x2+2)
- x/x2+2
- x/(x²+2)
- x/(x to the power of 2+2)
- x/x^2+2
- x divide by (x^2+2)
- x/(x^2+2)dx
-
Similar expressions
- x/(x^2-2)
- (2*x)/(x^2+2*x+2)^(1/2)
- xdx/x^2+2
- x/(x^2+2x+2)^2
Integral of x/(x^2+2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | x + 2 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} + 2}\, dx$$
Integral(x/(x^2 + 2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | x + 2 | /
Rewrite the integrand
/ 2*x \
|------------| /0\
| 2 | |-|
x \x + 0*x + 2/ \2/
------ = -------------- + ----------------
2 2 2
x + 2 / ___ \
|-\/ 2 |
|-------*x| + 1
\ 2 / or
/ | | x | ------ dx | 2 = | x + 2 | /
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 2
|
/
------------------
2 In the integral
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 2
|
/
------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
| ----- du
| 2 + u
|
/ log(2 + u)
----------- = ----------
2 2 do backward replacement
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 2
| / 2\
/ log\2 + x /
------------------ = -----------
2 2 In the integral
0
do replacement
___
-x*\/ 2
v = ---------
2 then
the integral =
True
do backward replacement
True
Solution is:
/ 2\
log\2 + x /
C + -----------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\2 + x / | ------ dx = C + ----------- | 2 2 | x + 2 | /
$$\int \frac{x}{x^{2} + 2}\, dx = C + \frac{\log{\left(x^{2} + 2 \right)}}{2}$$
The graph
The answer
[src]
log(3) log(2) ------ - ------ 2 2
$$- \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(3 \right)}}{2}$$
=
=
log(3) log(2) ------ - ------ 2 2
$$- \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(3 \right)}}{2}$$
log(3)/2 - log(2)/2
The graph
Use the examples entering the upper and lower limits of integration.