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How to use it?
- Integral of d{x}:
-
Integral of cosx
- Integral of (3-sin(x))/(2cos(x)+3tan(x))
-
Integral of x^(-6)
-
Integral of xe^(-5x)
-
Identical expressions
- two /(x²+4x+ eight)
- 2 divide by (x² plus 4x plus 8)
- two divide by (x² plus 4x plus eight)
- 2/x²+4x+8
- 2 divide by (x²+4x+8)
- 2/(x²+4x+8)dx
-
Similar expressions
- 2/(x²-4x+8)
- 2/(x²+4x-8)
Integral of 2/(x²+4x+8) dx
The solution
You have entered
[src]
oo / | | 2 | ------------ dx | 2 | x + 4*x + 8 | / 0
$$\int\limits_{0}^{\infty} \frac{2}{\left(x^{2} + 4 x\right) + 8}\, dx$$
Integral(2/(x^2 + 4*x + 8), (x, 0, oo))
Detail solution
We have the integral:
/ | | 2 | ------------ dx | 2 | x + 4*x + 8 | /
Rewrite the integrand
/2\
|-|
2 \4/
------------ = --------------
2 2
x + 4*x + 8 / x \
|- - - 1| + 1
\ 2 / or
/ | | 2 | ------------ dx | 2 = | x + 4*x + 8 | /
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 1| + 1
| \ 2 /
|
/
--------------------
2 In the integral
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 1| + 1
| \ 2 /
|
/
--------------------
2 do replacement
x
v = -1 - -
2then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
2 2 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 1| + 1
| \ 2 /
|
/ / x\
-------------------- = atan|1 + -|
2 \ 2/Solution is:
/ x\
C + atan|1 + -|
\ 2/
The answer (Indefinite)
[src]
/ | | 2 / x\ | ------------ dx = C + atan|1 + -| | 2 \ 2/ | x + 4*x + 8 | /
$$\int \frac{2}{\left(x^{2} + 4 x\right) + 8}\, dx = C + \operatorname{atan}{\left(\frac{x}{2} + 1 \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.