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How to use it?
- Integral of d{x}:
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Integral of (-1)/x^2
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Integral of x⁴
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Integral of 2e^x
- Integral of e^(x/y)
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Identical expressions
- one /(x^ two +8x+ seventeen)
- 1 divide by (x squared plus 8x plus 17)
- one divide by (x to the power of two plus 8x plus seventeen)
- 1/(x2+8x+17)
- 1/x2+8x+17
- 1/(x²+8x+17)
- 1/(x to the power of 2+8x+17)
- 1/x^2+8x+17
- 1 divide by (x^2+8x+17)
- 1/(x^2+8x+17)dx
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Similar expressions
- 1/(x^2+8x-17)
- 1/(x^2-8x+17)
Integral of 1/(x^2+8x+17) dx
The solution
You have entered
[src]
oo / | | 1 | 1*------------- dx | 2 | x + 8*x + 17 | / -oo
$$\int\limits_{-\infty}^{\infty} 1 \cdot \frac{1}{x^{2} + 8 x + 17}\, dx$$
Integral(1/(x^2 + 8*x + 17), (x, -oo, oo))
Detail solution
We have the integral:
/ | | 1 | 1*1*------------- dx | 2 | x + 8*x + 17 | /
Rewrite the integrand
1 1 1*------------- = ----------------- 2 / 2 \ x + 8*x + 17 1*\(-x - 4) + 1/
or
/ | | 1 | 1*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 | 1*------------- dx = C + atan(4 + x) | 2 | x + 8*x + 17 | /
$$\arctan \left({{2\,x+8}\over{2}}\right)$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.