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