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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sint
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Integral of sin(3x)*cos(5x)
- Integral of 1/(4sin^2x+9cos^2x)
- Integral of (x+cosx)/(x^2+2sinx)
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Identical expressions
- one /(x^ two +10x+ twenty-six)
- 1 divide by (x squared plus 10x plus 26)
- one divide by (x to the power of two plus 10x plus twenty minus six)
- 1/(x2+10x+26)
- 1/x2+10x+26
- 1/(x²+10x+26)
- 1/(x to the power of 2+10x+26)
- 1/x^2+10x+26
- 1 divide by (x^2+10x+26)
- 1/(x^2+10x+26)dx
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Similar expressions
- 1/(x^2+10x-26)
- 1/(x^2-10x+26)
Integral of 1/(x^2+10x+26) dx
The solution
You have entered
[src]
0 / | | 1 | -------------- dx | 2 | x + 10*x + 26 | / -oo
$$\int\limits_{-\infty}^{0} \frac{1}{\left(x^{2} + 10 x\right) + 26}\, dx$$
Integral(1/(x^2 + 10*x + 26), (x, -oo, 0))
Detail solution
We have the integral:
/ | | 1 | -------------- dx | 2 | x + 10*x + 26 | /
Rewrite the integrand
1 1 -------------- = ----------------- 2 / 2 \ x + 10*x + 26 1*\(-x - 5) + 1/
or
/ | | 1 | -------------- dx | 2 = | x + 10*x + 26 | /
/ | | 1 | ------------- dx | 2 | (-x - 5) + 1 | /
In the integral
/ | | 1 | ------------- dx | 2 | (-x - 5) + 1 | /
do replacement
v = -5 - x
then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 | ------------- dx = atan(5 + x) | 2 | (-x - 5) + 1 | /
Solution is:
C + atan(5 + x)
The answer (Indefinite)
[src]
/ | | 1 | -------------- dx = C + atan(5 + x) | 2 | x + 10*x + 26 | /
$$\int \frac{1}{\left(x^{2} + 10 x\right) + 26}\, dx = C + \operatorname{atan}{\left(x + 5 \right)}$$
The graph
The answer
[src]
pi -- + atan(5) 2
$$\operatorname{atan}{\left(5 \right)} + \frac{\pi}{2}$$
=
=
pi -- + atan(5) 2
$$\operatorname{atan}{\left(5 \right)} + \frac{\pi}{2}$$
pi/2 + atan(5)
Use the examples entering the upper and lower limits of integration.