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- Integral of d{x}:
- Integral of 1/x^n
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Integral of sin(x²)
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Integral of (9-x^2)^(1/2)
- Integral of 1/(x+sqrt(x^2+x+1))
-
Identical expressions
- one /(x^ two -6x+ one hundred)
- 1 divide by (x squared minus 6x plus 100)
- one divide by (x to the power of two minus 6x plus one hundred)
- 1/(x2-6x+100)
- 1/x2-6x+100
- 1/(x²-6x+100)
- 1/(x to the power of 2-6x+100)
- 1/x^2-6x+100
- 1 divide by (x^2-6x+100)
- 1/(x^2-6x+100)dx
-
Similar expressions
- 1/(x^2+6x+100)
- 1/(x^2-6x-100)
Integral of 1/(x^2-6x+100) dx
The solution
You have entered
[src]
oo / | | 1 | -------------- dx | 2 | x - 6*x + 100 | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\left(x^{2} - 6 x\right) + 100}\, dx$$
Integral(1/(x^2 - 6*x + 100), (x, 2, oo))
Detail solution
We have the integral:
/ | | 1 | -------------- dx | 2 | x - 6*x + 100 | /
Rewrite the integrand
1 1
-------------- = ---------------------------------
2 / 2 \
x - 6*x + 100 |/ ____ ____\ |
||-\/ 91 3*\/ 91 | |
91*||--------*x + --------| + 1|
\\ 91 91 / /or
/ | | 1 | -------------- dx | 2 = | x - 6*x + 100 | /
/
|
| 1
| ---------------------------- dx
| 2
| / ____ ____\
| |-\/ 91 3*\/ 91 |
| |--------*x + --------| + 1
| \ 91 91 /
|
/
----------------------------------
91 In the integral
/
|
| 1
| ---------------------------- dx
| 2
| / ____ ____\
| |-\/ 91 3*\/ 91 |
| |--------*x + --------| + 1
| \ 91 91 /
|
/
----------------------------------
91 do replacement
____ ____
3*\/ 91 x*\/ 91
v = -------- - --------
91 91 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
91 91 do backward replacement
/
|
| 1
| ---------------------------- dx
| 2
| / ____ ____\
| |-\/ 91 3*\/ 91 |
| |--------*x + --------| + 1 / ____ ____\
| \ 91 91 / ____ | 3*\/ 91 x*\/ 91 |
| \/ 91 *atan|- -------- + --------|
/ \ 91 91 /
---------------------------------- = ----------------------------------
91 91 Solution is:
/ ____ ____\
____ | 3*\/ 91 x*\/ 91 |
\/ 91 *atan|- -------- + --------|
\ 91 91 /
C + ----------------------------------
91
The answer (Indefinite)
[src]
/ ____ \ / ____ |\/ 91 *(-3 + x)| | \/ 91 *atan|---------------| | 1 \ 91 / | -------------- dx = C + ---------------------------- | 2 91 | x - 6*x + 100 | /
$$\int \frac{1}{\left(x^{2} - 6 x\right) + 100}\, dx = C + \frac{\sqrt{91} \operatorname{atan}{\left(\frac{\sqrt{91} \left(x - 3\right)}{91} \right)}}{91}$$
The graph
The answer
[src]
/ ____\
____ |\/ 91 |
\/ 91 *atan|------| ____
\ 91 / pi*\/ 91
------------------- + ---------
91 182
$$\frac{\sqrt{91} \operatorname{atan}{\left(\frac{\sqrt{91}}{91} \right)}}{91} + \frac{\sqrt{91} \pi}{182}$$
=
=
/ ____\
____ |\/ 91 |
\/ 91 *atan|------| ____
\ 91 / pi*\/ 91
------------------- + ---------
91 182
$$\frac{\sqrt{91} \operatorname{atan}{\left(\frac{\sqrt{91}}{91} \right)}}{91} + \frac{\sqrt{91} \pi}{182}$$
sqrt(91)*atan(sqrt(91)/91)/91 + pi*sqrt(91)/182
Use the examples entering the upper and lower limits of integration.