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-
How to use it?
- Integral of d{x}:
-
Integral of -1/y
-
Integral of e^(-x/2)
-
Integral of (x^2+1)e^-x
-
Integral of 4^(2*x)
- Graphing y =:
- x/(9+x^2)
- Limit of the function:
-
x/(9+x^2)
-
Identical expressions
- x/(nine +x^ two)
- x divide by (9 plus x squared )
- x divide by (nine plus 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/(9-x^2)
Integral of x/(9+x^2) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 2 | 9 + x | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{2} + 9}\, dx$$
Integral(x/(9 + x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | ------ dx | 2 | 9 + x | /
Rewrite the integrand
/ 2*x \
|------------| /0\
| 2 | |-|
x \x + 0*x + 9/ \9/
------ = -------------- + ----------
2 2 2
9 + x /-x \
|---| + 1
\ 3 / 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 In the integral
0
do replacement
-x
v = ---
3 then
the integral =
True
do backward replacement
True
Solution is:
/ 2\
log\9 + x /
C + -----------
2
The answer (Indefinite)
[src]
/ | / 2\ | x log\9 + x / | ------ dx = C + ----------- | 2 2 | 9 + x | /
$$\int \frac{x}{x^{2} + 9}\, dx = C + \frac{\log{\left(x^{2} + 9 \right)}}{2}$$
The graph
The answer
[src]
log(10) log(9) ------- - ------ 2 2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(10 \right)}}{2}$$
=
=
log(10) log(9) ------- - ------ 2 2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(10 \right)}}{2}$$
log(10)/2 - log(9)/2
The graph
Use the examples entering the upper and lower limits of integration.