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How to use it?
- Integral of d{x}:
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Integral of tg2x
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Integral of xsqrt(x²+1)
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Integral of x^3*e^(x*(-2))
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Integral of (x^3-1)^1/2
- Limit of the function:
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x/(2+x^2)
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Identical expressions
- x/(two +x^ two)
- x divide by (2 plus x squared )
- x divide by (two plus x to the power of two)
- x/(2+x2)
- x/2+x2
- x/(2+x²)
- x/(2+x to the power of 2)
- x/2+x^2
- x divide by (2+x^2)
- x/(2+x^2)dx
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Similar expressions
- x/(2-x^2)
Integral of x/(2+x^2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | 2 + x | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} + 2}\, dx$$
Integral(x/(2 + x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | 2 + x | /
Rewrite the integrand
/ 2*x \
|------------| /0\
| 2 | |-|
x \x + 0*x + 2/ \2/
------ = -------------- + ----------------
2 2 2
2 + x / ___ \
|-\/ 2 |
|-------*x| + 1
\ 2 / or
/ | | x | ------ dx | 2 = | 2 + x | /
/
|
| 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 | 2 + x | /
$$\int \frac{x}{x^{2} + 2}\, dx = C + \frac{\log{\left(x^{2} + 2 \right)}}{2}$$
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.