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