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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (1+x)/x
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Integral of e^3
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Integral of (x+1)^4
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Integral of (sec(x))^3
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Identical expressions
- dx/(x^ two -4x+ five)
- dx divide by (x squared minus 4x plus 5)
- dx divide by (x to the power of two minus 4x plus five)
- dx/(x2-4x+5)
- dx/x2-4x+5
- dx/(x²-4x+5)
- dx/(x to the power of 2-4x+5)
- dx/x^2-4x+5
- dx divide by (x^2-4x+5)
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Similar expressions
- dx/(x^2-4x-5)
- dx/(x^2+4x+5)
Integral of dx/(x^2-4x+5) dx
The solution
You have entered
[src]
2 / | | 1 | ------------ dx | 2 | x - 4*x + 5 | / 0
$$\int\limits_{0}^{2} \frac{1}{\left(x^{2} - 4 x\right) + 5}\, dx$$
Integral(1/(x^2 - 4*x + 5), (x, 0, 2))
Detail solution
We have the integral:
/ | | 1 | ------------ dx | 2 | x - 4*x + 5 | /
Rewrite the integrand
1 1 ------------ = ----------------- 2 / 2 \ x - 4*x + 5 1*\(-x + 2) + 1/
or
/ | | 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 | ------------ dx = C + atan(-2 + x) | 2 | x - 4*x + 5 | /
$$\int \frac{1}{\left(x^{2} - 4 x\right) + 5}\, dx = C + \operatorname{atan}{\left(x - 2 \right)}$$
The graph
The answer
[src]
atan(2)
$$\operatorname{atan}{\left(2 \right)}$$
=
=
atan(2)
$$\operatorname{atan}{\left(2 \right)}$$
atan(2)
Use the examples entering the upper and lower limits of integration.