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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of x/y
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Integral of exp(2x)
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Integral of dx/(1+e^x)
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Integral of 1/(1+x^2)^1/2
- Graphing y =:
- 8/(x^2+4)
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Identical expressions
- eight /(x^ two + four)
- 8 divide by (x squared plus 4)
- eight divide by (x to the power of two plus four)
- 8/(x2+4)
- 8/x2+4
- 8/(x²+4)
- 8/(x to the power of 2+4)
- 8/x^2+4
- 8 divide by (x^2+4)
- 8/(x^2+4)dx
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Similar expressions
- 8/(x^2-4)
Integral of 8/(x^2+4) dx
The solution
You have entered
[src]
1 / | | 8 | ------ dx | 2 | x + 4 | / 0
$$\int\limits_{0}^{1} \frac{8}{x^{2} + 4}\, dx$$
Integral(8/(x^2 + 4), (x, 0, 1))
Detail solution
We have the integral:
/ | | 8 | ------ dx | 2 | x + 4 | /
Rewrite the integrand
/8\
|-|
8 \4/
------ = ----------
2 2
x + 4 /-x \
|---| + 1
\ 2 / or
/ | | 8 | ------ dx | 2 = | x + 4 | /
/ | | 1 2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 2 / | /
In the integral
/ | | 1 2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 2 / | /
do replacement
-x
v = ---
2 then
the integral =
/ | | 1 2* | ------ dv = 2*atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 /x\ 2* | ---------- dx = 4*atan|-| | 2 \2/ | /-x \ | |---| + 1 | \ 2 / | /
Solution is:
/x\
C + 4*atan|-|
\2/
The answer (Indefinite)
[src]
/ | | 8 /x\ | ------ dx = C + 4*atan|-| | 2 \2/ | x + 4 | /
$$\int \frac{8}{x^{2} + 4}\, dx = C + 4 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
The graph
The answer
[src]
4*atan(1/2)
$$4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
=
4*atan(1/2)
$$4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
4*atan(1/2)
The graph
Use the examples entering the upper and lower limits of integration.