Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of 1/(2+x^2)
- Integral of x/(x^3-3x+2)
-
Integral of -x+4
-
Integral of 8/x^2
- Derivative of:
- 1/(2+x^2)
- Limit of the function:
-
1/(2+x^2)
-
Identical expressions
- one /(two +x^ two)
- 1 divide by (2 plus x squared )
- one divide by (two plus x to the power of two)
- 1/(2+x2)
- 1/2+x2
- 1/(2+x²)
- 1/(2+x to the power of 2)
- 1/2+x^2
- 1 divide by (2+x^2)
- 1/(2+x^2)dx
-
Similar expressions
- 1/(2-x^2)
Integral of 1/(2+x^2) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 2 | 2 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 2}\, dx$$
Integral(1/(2 + x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------ dx | 2 | 2 + x | /
Rewrite the integrand
1 1
------ = --------------------
2 / 2 \
2 + x |/ ___ \ |
||-\/ 2 | |
2*||-------*x| + 1|
\\ 2 / /or
/ | | 1 | ------ dx | 2 = | 2 + x | /
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 2 |
| |-------*x| + 1
| \ 2 /
|
/
----------------------
2 In the integral
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 2 |
| |-------*x| + 1
| \ 2 /
|
/
----------------------
2 do replacement
___
-x*\/ 2
v = ---------
2 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
2 2 do backward replacement
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 2 |
| |-------*x| + 1 / ___\
| \ 2 / ___ |x*\/ 2 |
| \/ 2 *atan|-------|
/ \ 2 /
---------------------- = -------------------
2 2 Solution is:
/ ___\
___ |x*\/ 2 |
\/ 2 *atan|-------|
\ 2 /
C + -------------------
2
The answer (Indefinite)
[src]
/ ___\ / ___ |x*\/ 2 | | \/ 2 *atan|-------| | 1 \ 2 / | ------ dx = C + ------------------- | 2 2 | 2 + x | /
$$\int \frac{1}{x^{2} + 2}\, dx = C + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$
The graph
The answer
[src]
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----|
\ 2 /
-----------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$
=
=
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----|
\ 2 /
-----------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$
sqrt(2)*atan(sqrt(2)/2)/2
The graph
Use the examples entering the upper and lower limits of integration.