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- Improper integral
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How to use it?
- Integral of d{x}:
-
Integral of x^2*e^(x*(-2))
-
Integral of (x^3+1)^1/2
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Integral of 1/(1+sqrt(x+1))
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Integral of xdx/(x^2+2)^5
- Limit of the function:
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3*x/(2+x^2)
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Identical expressions
- three *x/(two +x^ two)
- 3 multiply by x divide by (2 plus x squared )
- three multiply by x divide by (two plus x to the power of two)
- 3*x/(2+x2)
- 3*x/2+x2
- 3*x/(2+x²)
- 3*x/(2+x to the power of 2)
- 3x/(2+x^2)
- 3x/(2+x2)
- 3x/2+x2
- 3x/2+x^2
- 3*x divide by (2+x^2)
- 3*x/(2+x^2)dx
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Similar expressions
- 3*x/(2-x^2)
Integral of 3*x/(2+x^2) dx
The solution
You have entered
[src]
1 / | | 3*x | ------ dx | 2 | 2 + x | / -1
$$\int\limits_{-1}^{1} \frac{3 x}{x^{2} + 2}\, dx$$
Integral((3*x)/(2 + x^2), (x, -1, 1))
Detail solution
We have the integral:
/ | | 3*x | ------ dx | 2 | 2 + x | /
Rewrite the integrand
2*x
3*------------ /0\
2 |-|
3*x x + 0*x + 2 \2/
------ = -------------- + ----------------
2 2 2
2 + x / ___ \
|-\/ 2 |
|-------*x| + 1
\ 2 / or
/ | | 3*x | ------ dx | 2 = | 2 + x | /
/
|
| 2*x
3* | ------------ dx
| 2
| x + 0*x + 2
|
/
--------------------
2 In the integral
/
|
| 2*x
3* | ------------ dx
| 2
| x + 0*x + 2
|
/
--------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
3* | ----- du
| 2 + u
|
/ 3*log(2 + u)
------------- = ------------
2 2 do backward replacement
/
|
| 2*x
3* | ------------ dx
| 2
| x + 0*x + 2
| / 2\
/ 3*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\
3*log\2 + x /
C + -------------
2
The answer (Indefinite)
[src]
/ | / 2\ | 3*x 3*log\2 + x / | ------ dx = C + ------------- | 2 2 | 2 + x | /
$$\int \frac{3 x}{x^{2} + 2}\, dx = C + \frac{3 \log{\left(x^{2} + 2 \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.