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