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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of tan^3(5x)
- Integral of sinh(ax)
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Integral of sin8x*cos3x
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Integral of 1/3*t^3*dt
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Identical expressions
- dx/(x^ two -8x+ seventeen)
- dx divide by (x squared minus 8x plus 17)
- dx divide by (x to the power of two minus 8x plus seventeen)
- dx/(x2-8x+17)
- dx/x2-8x+17
- dx/(x²-8x+17)
- dx/(x to the power of 2-8x+17)
- dx/x^2-8x+17
- dx divide by (x^2-8x+17)
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Similar expressions
- dx/(x^2-8x-17)
- dx/(x^2+8x+17)
Integral of dx/(x^2-8x+17) dx
The solution
You have entered
[src]
oo / | | 1 | ------------- dx | 2 | x - 8*x + 17 | / 5
$$\int\limits_{5}^{\infty} \frac{1}{\left(x^{2} - 8 x\right) + 17}\, dx$$
Integral(1/(x^2 - 8*x + 17), (x, 5, oo))
Detail solution
We have the integral:
/ | | 1 | ------------- dx | 2 | x - 8*x + 17 | /
Rewrite the integrand
1 1 ------------- = ----------------- 2 / 2 \ x - 8*x + 17 1*\(-x + 4) + 1/
or
/ | | 1 | ------------- dx | 2 = | x - 8*x + 17 | /
/ | | 1 | ------------- dx | 2 | (-x + 4) + 1 | /
In the integral
/ | | 1 | ------------- dx | 2 | (-x + 4) + 1 | /
do replacement
v = 4 - x
then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 | ------------- dx = atan(-4 + x) | 2 | (-x + 4) + 1 | /
Solution is:
C + atan(-4 + x)
The answer (Indefinite)
[src]
/ | | 1 | ------------- dx = C + atan(-4 + x) | 2 | x - 8*x + 17 | /
$$\int \frac{1}{\left(x^{2} - 8 x\right) + 17}\, dx = C + \operatorname{atan}{\left(x - 4 \right)}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.