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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 1÷(x^2-1)
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Integral of cos(x)^(-2)
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Integral of exp(7*x)*sin(x)
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Integral of 1/(x^2+2*x+5)
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Identical expressions
- one /(x^ two + two *x+ five)
- 1 divide by (x squared plus 2 multiply by x plus 5)
- one divide by (x to the power of two plus two multiply by x plus five)
- 1/(x2+2*x+5)
- 1/x2+2*x+5
- 1/(x²+2*x+5)
- 1/(x to the power of 2+2*x+5)
- 1/(x^2+2x+5)
- 1/(x2+2x+5)
- 1/x2+2x+5
- 1/x^2+2x+5
- 1 divide by (x^2+2*x+5)
- 1/(x^2+2*x+5)dx
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Similar expressions
- 1/(x^2-2*x+5)
- 1/(x^2+2*x-5)
Integral of 1/(x^2+2*x+5) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 2 | x + 2*x + 5 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 2 x\right) + 5}\, dx$$
Integral(1/(x^2 + 2*x + 5), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------------ dx | 2 | x + 2*x + 5 | /
Rewrite the integrand
1 1
------------ = ------------------
2 / 2 \
x + 2*x + 5 |/ x 1\ |
4*||- - - -| + 1|
\\ 2 2/ /or
/ | | 1 | ------------ dx | 2 = | x + 2*x + 5 | /
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - - -| + 1
| \ 2 2/
|
/
--------------------
4 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - - -| + 1
| \ 2 2/
|
/
--------------------
4 do replacement
1 x
v = - - - -
2 2then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
4 4 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - - -| + 1
| \ 2 2/ /1 x\
| atan|- + -|
/ \2 2/
-------------------- = -----------
4 2 Solution is:
/1 x\
atan|- + -|
\2 2/
C + -----------
2
The answer (Indefinite)
[src]
/ /1 x\ | atan|- + -| | 1 \2 2/ | ------------ dx = C + ----------- | 2 2 | x + 2*x + 5 | /
$$\int \frac{1}{\left(x^{2} + 2 x\right) + 5}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{2} + \frac{1}{2} \right)}}{2}$$
The graph
The answer
[src]
atan(1/2) pi
- --------- + --
2 8
$$- \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \frac{\pi}{8}$$
=
=
atan(1/2) pi
- --------- + --
2 8
$$- \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \frac{\pi}{8}$$
-atan(1/2)/2 + pi/8
The graph
Use the examples entering the upper and lower limits of integration.