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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^2/x
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Integral of cos^2(4x)
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Integral of (2x-3)^4
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Integral of -2cosx
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Identical expressions
- (3x- seventeen)/(x^ two -6x+ ten)
- (3x minus 17) divide by (x squared minus 6x plus 10)
- (3x minus seventeen) divide by (x to the power of two minus 6x plus ten)
- (3x-17)/(x2-6x+10)
- 3x-17/x2-6x+10
- (3x-17)/(x²-6x+10)
- (3x-17)/(x to the power of 2-6x+10)
- 3x-17/x^2-6x+10
- (3x-17) divide by (x^2-6x+10)
- (3x-17)/(x^2-6x+10)dx
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Similar expressions
- (3x-17)/(x^2-6x-10)
- (3x+17)/(x^2-6x+10)
- (3x-17)/(x^2+6x+10)
Integral of (3x-17)/(x^2-6x+10) dx
The solution
You have entered
[src]
3 / | | 3*x - 17 | ------------- dx | 2 | x - 6*x + 10 | / 2
$$\int\limits_{2}^{3} \frac{3 x - 17}{x^{2} - 6 x + 10}\, dx$$
Integral((3*x - 1*17)/(x^2 - 6*x + 10), (x, 2, 3))
Detail solution
We have the integral:
/ | | 3*x - 17 | 1*------------- dx | 2 | x - 6*x + 10 | /
Rewrite the integrand
1*2*x - 6
3*--------------- /-8 \
2 |---|
3*x - 17 1*x - 6*x + 10 \ 1 /
------------- = ----------------- + -------------
2 2 2
x - 6*x + 10 (-x + 3) + 1or
/ | | 3*x - 17 | 1*------------- dx | 2 = | x - 6*x + 10 | /
/
|
| 1*2*x - 6
3* | --------------- dx
| 2
/ | 1*x - 6*x + 10
| |
| 1 /
- 8* | ------------- dx + -----------------------
| 2 2
| (-x + 3) + 1
|
/ In the integral
/
|
| 1*2*x - 6
3* | --------------- dx
| 2
| 1*x - 6*x + 10
|
/
-----------------------
2 do replacement
2 u = x - 6*x
then
the integral =
/
|
| 1
3* | ------ du
| 10 + u
|
/ 3*log(10 + u)
-------------- = -------------
2 2 do backward replacement
/
|
| 1*2*x - 6
3* | --------------- dx
| 2
| 1*x - 6*x + 10
| / 2 \
/ 3*log\10 + x - 6*x/
----------------------- = --------------------
2 2 In the integral
/
|
| 1
-8* | ------------- dx
| 2
| (-x + 3) + 1
|
/ do replacement
v = 3 - x
then
the integral =
/
|
| 1
-8* | ------ dv = -8*atan(v)
| 2
| 1 + v
|
/ do backward replacement
/
|
| 1
-8* | ------------- dx = -8*atan(-3 + x)
| 2
| (-x + 3) + 1
|
/ Solution is:
/ 2 \
3*log\10 + x - 6*x/
C - 8*atan(-3 + x) + --------------------
2
The answer (Indefinite)
[src]
/ | / 2 \ | 3*x - 17 3*log\10 + x - 6*x/ | ------------- dx = C - 8*atan(-3 + x) + -------------------- | 2 2 | x - 6*x + 10 | /
$${{3\,\log \left(x^2-6\,x+10\right)}\over{2}}-8\,\arctan \left({{2\,
x-6}\over{2}}\right)$$
The graph
The answer
[src]
3*log(2)
-2*pi - --------
2
$$-{{3\,\log 2}\over{2}}-2\,\pi$$
=
=
3*log(2)
-2*pi - --------
2
$$- 2 \pi - \frac{3 \log{\left(2 \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.