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- Improper integral
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-
How to use it?
- Integral of d{x}:
-
Integral of e^(2*x+1)
-
Integral of dx/(9*x^2-1)
-
Integral of -cos(2x)
-
Integral of dx/(5-2*x)
- Graphing y =:
- x/(3-x^2)
- Limit of the function:
-
x/(3-x^2)
-
Identical expressions
- x/(three -x^ two)
- x divide by (3 minus x squared )
- x divide by (three minus x to the power of two)
- x/(3-x2)
- x/3-x2
- x/(3-x²)
- x/(3-x to the power of 2)
- x/3-x^2
- x divide by (3-x^2)
- x/(3-x^2)dx
-
Similar expressions
- x/(3+x^2)
Integral of x/(3-x^2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | 3 - x | / 0
$$\int\limits_{0}^{1} \frac{x}{3 - x^{2}}\, dx$$
Integral(x/(3 - x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | 3 - x | /
Rewrite the integrand
-2*x
- --------------
2
x - x + 0*x + 3
------ = -----------------
2 2
3 - x or
/ | | x | ------ dx | 2 = | 3 - x | /
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 3
|
/
----------------------
2 In the integral
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 3
|
/
----------------------
2 do replacement
2 u = -x
then
the integral =
/
|
| 1
- | ----- du
| 3 + u
|
/ -log(3 + u)
------------- = ------------
2 2 do backward replacement
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 3
| / 2\
/ -log\-3 + x /
---------------------- = --------------
2 2 Solution is:
/ 2\
log\-3 + x /
C - ------------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\3 - x / | ------ dx = C - ----------- | 2 2 | 3 - x | /
$$\int \frac{x}{3 - x^{2}}\, dx = C - \frac{\log{\left(3 - x^{2} \right)}}{2}$$
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.