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How to use it?
- Integral of d{x}:
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Integral of e^(2*x)*cos(3*x)
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Integral of (2x-4)
- Integral of (3-sin(x))/(2cos(x)+3tan(x))
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Integral of 1/(x^2+2x+1)
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Identical expressions
- one /(x^ two - two *x+ ten)
- 1 divide by (x squared minus 2 multiply by x plus 10)
- one divide by (x to the power of two minus two multiply by x plus ten)
- 1/(x2-2*x+10)
- 1/x2-2*x+10
- 1/(x²-2*x+10)
- 1/(x to the power of 2-2*x+10)
- 1/(x^2-2x+10)
- 1/(x2-2x+10)
- 1/x2-2x+10
- 1/x^2-2x+10
- 1 divide by (x^2-2*x+10)
- 1/(x^2-2*x+10)dx
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Similar expressions
- 1/(x^2-2*x-10)
- 1/(x^2+2*x+10)
Integral of 1/(x^2-2*x+10) dx
The solution
You have entered
[src]
oo / | | 1 | ------------- dx | 2 | x - 2*x + 10 | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{1}{\left(x^{2} - 2 x\right) + 10}\, dx$$
Integral(1/(x^2 - 2*x + 10), (x, -oo, oo))
Detail solution
We have the integral:
/ | | 1 | ------------- dx | 2 | x - 2*x + 10 | /
Rewrite the integrand
1 1
------------- = ------------------
2 / 2 \
x - 2*x + 10 |/ x 1\ |
9*||- - + -| + 1|
\\ 3 3/ /or
/ | | 1 | ------------- dx | 2 = | x - 2*x + 10 | /
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - + -| + 1
| \ 3 3/
|
/
--------------------
9 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - + -| + 1
| \ 3 3/
|
/
--------------------
9 do replacement
1 x
v = - - -
3 3then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
9 9 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 1\
| |- - + -| + 1
| \ 3 3/ / 1 x\
| atan|- - + -|
/ \ 3 3/
-------------------- = -------------
9 3 Solution is:
/ 1 x\
atan|- - + -|
\ 3 3/
C + -------------
3
The answer (Indefinite)
[src]
/ / 1 x\ | atan|- - + -| | 1 \ 3 3/ | ------------- dx = C + ------------- | 2 3 | x - 2*x + 10 | /
$$\int \frac{1}{\left(x^{2} - 2 x\right) + 10}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{1}{3} \right)}}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.