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- Improper integral
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-
How to use it?
- Integral of d{x}:
-
Integral of -e^x
-
Integral of -15x^2
-
Integral of xe^(1-x)
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Integral of -xe^x
- Derivative of:
-
x/(9-x^2)
- Limit of the function:
-
x/(9-x^2)
-
Identical expressions
- x/(nine -x^ two)
- x divide by (9 minus x squared )
- x divide by (nine minus x to the power of two)
- x/(9-x2)
- x/9-x2
- x/(9-x²)
- x/(9-x to the power of 2)
- x/9-x^2
- x divide by (9-x^2)
- x/(9-x^2)dx
-
Similar expressions
- x^2*dx/(9-x)^2
- x/(9+x^2)
Integral of x/(9-x^2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | 9 - x | / 0
$$\int\limits_{0}^{1} \frac{x}{9 - x^{2}}\, dx$$
Integral(x/(9 - x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | 9 - x | /
Rewrite the integrand
-2*x
- --------------
2
x - x + 0*x + 9
------ = -----------------
2 2
9 - x or
/ | | x | ------ dx | 2 = | 9 - x | /
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 9
|
/
----------------------
2 In the integral
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 9
|
/
----------------------
2 do replacement
2 u = -x
then
the integral =
/
|
| 1
- | ----- du
| 9 + u
|
/ -log(9 + u)
------------- = ------------
2 2 do backward replacement
/
|
| -2*x
- | -------------- dx
| 2
| - x + 0*x + 9
| / 2\
/ -log\-9 + x /
---------------------- = --------------
2 2 Solution is:
/ 2\
log\-9 + x /
C - ------------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\9 - x / | ------ dx = C - ----------- | 2 2 | 9 - x | /
$$\int \frac{x}{9 - x^{2}}\, dx = C - \frac{\log{\left(9 - x^{2} \right)}}{2}$$
The graph
The answer
[src]
log(9) log(8) ------ - ------ 2 2
$$- \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(9 \right)}}{2}$$
=
=
log(9) log(8) ------ - ------ 2 2
$$- \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(9 \right)}}{2}$$
log(9)/2 - log(8)/2
The graph
Use the examples entering the upper and lower limits of integration.