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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
-
Integral of x+
- Integral of log(1+x)/x^2
- Integral of x/sqrt(x^2-4x+1)
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Integral of x/(x^2-1)^3
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Identical expressions
- one /(x^ two -4x+ seven)
- 1 divide by (x squared minus 4x plus 7)
- one divide by (x to the power of two minus 4x plus seven)
- 1/(x2-4x+7)
- 1/x2-4x+7
- 1/(x²-4x+7)
- 1/(x to the power of 2-4x+7)
- 1/x^2-4x+7
- 1 divide by (x^2-4x+7)
- 1/(x^2-4x+7)dx
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Similar expressions
- 1/(x^2-4x-7)
- 1/(x^2+4x+7)
Integral of 1/(x^2-4x+7) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 2 | x - 4*x + 7 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 4 x\right) + 7}\, dx$$
Integral(1/(x^2 - 4*x + 7), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------------ dx | 2 | x - 4*x + 7 | /
Rewrite the integrand
1 1
------------ = ------------------------------
2 / 2 \
x - 4*x + 7 |/ ___ ___\ |
||-\/ 3 2*\/ 3 | |
3*||-------*x + -------| + 1|
\\ 3 3 / /or
/ | | 1 | ------------ dx | 2 = | x - 4*x + 7 | /
/
|
| 1
| -------------------------- dx
| 2
| / ___ ___\
| |-\/ 3 2*\/ 3 |
| |-------*x + -------| + 1
| \ 3 3 /
|
/
--------------------------------
3 In the integral
/
|
| 1
| -------------------------- dx
| 2
| / ___ ___\
| |-\/ 3 2*\/ 3 |
| |-------*x + -------| + 1
| \ 3 3 /
|
/
--------------------------------
3 do replacement
___ ___
2*\/ 3 x*\/ 3
v = ------- - -------
3 3 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
3 3 do backward replacement
/
|
| 1
| -------------------------- dx
| 2
| / ___ ___\
| |-\/ 3 2*\/ 3 |
| |-------*x + -------| + 1 / ___ ___\
| \ 3 3 / ___ | 2*\/ 3 x*\/ 3 |
| \/ 3 *atan|- ------- + -------|
/ \ 3 3 /
-------------------------------- = -------------------------------
3 3 Solution is:
/ ___ ___\
___ | 2*\/ 3 x*\/ 3 |
\/ 3 *atan|- ------- + -------|
\ 3 3 /
C + -------------------------------
3
The answer (Indefinite)
[src]
/ ___ \ / ___ |\/ 3 *(-2 + x)| | \/ 3 *atan|--------------| | 1 \ 3 / | ------------ dx = C + -------------------------- | 2 3 | x - 4*x + 7 | /
$$\int \frac{1}{\left(x^{2} - 4 x\right) + 7}\, dx = C + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3} \right)}}{3}$$
The graph
The answer
[src]
/ ___\
___ |2*\/ 3 |
___ \/ 3 *atan|-------|
pi*\/ 3 \ 3 /
- -------- + -------------------
18 3
$$- \frac{\sqrt{3} \pi}{18} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{3}$$
=
=
/ ___\
___ |2*\/ 3 |
___ \/ 3 *atan|-------|
pi*\/ 3 \ 3 /
- -------- + -------------------
18 3
$$- \frac{\sqrt{3} \pi}{18} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{3}$$
-pi*sqrt(3)/18 + sqrt(3)*atan(2*sqrt(3)/3)/3
The graph
Use the examples entering the upper and lower limits of integration.