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