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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/(x^2-8x+25)
- Integral of 3x^3+const
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Integral of 1/(x*sqrt(ln(x)))
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Integral of sqrt(4x^2-4x+3)
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Identical expressions
- one /(x^ two -8x+ twenty-five)
- 1 divide by (x squared minus 8x plus 25)
- one divide by (x to the power of two minus 8x plus twenty minus five)
- 1/(x2-8x+25)
- 1/x2-8x+25
- 1/(x²-8x+25)
- 1/(x to the power of 2-8x+25)
- 1/x^2-8x+25
- 1 divide by (x^2-8x+25)
- 1/(x^2-8x+25)dx
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Similar expressions
- 1/(x^2+8x+25)
- 1/(x^2-8x-25)
Integral of 1/(x^2-8x+25) dx
The solution
You have entered
[src]
1 / | | 1 | ------------- dx | 2 | x - 8*x + 25 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 8 x\right) + 25}\, dx$$
Integral(1/(x^2 - 8*x + 25), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------------- dx | 2 | x - 8*x + 25 | /
Rewrite the integrand
1 1
------------- = ------------------
2 / 2 \
x - 8*x + 25 |/ x 4\ |
9*||- - + -| + 1|
\\ 3 3/ /or
/ | | 1 | ------------- dx | 2 = | x - 8*x + 25 | /
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - + -| + 1
| \ 3 3/
|
/
--------------------
9 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - + -| + 1
| \ 3 3/
|
/
--------------------
9 do replacement
4 x
v = - - -
3 3then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
9 9 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - + -| + 1
| \ 3 3/ / 4 x\
| atan|- - + -|
/ \ 3 3/
-------------------- = -------------
9 3 Solution is:
/ 4 x\
atan|- - + -|
\ 3 3/
C + -------------
3
The answer (Indefinite)
[src]
/ / 4 x\ | atan|- - + -| | 1 \ 3 3/ | ------------- dx = C + ------------- | 2 3 | x - 8*x + 25 | /
$$\int \frac{1}{\left(x^{2} - 8 x\right) + 25}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{4}{3} \right)}}{3}$$
The graph
The answer
[src]
pi atan(4/3) - -- + --------- 12 3
$$- \frac{\pi}{12} + \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{3}$$
=
=
pi atan(4/3) - -- + --------- 12 3
$$- \frac{\pi}{12} + \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{3}$$
-pi/12 + atan(4/3)/3
The graph
Use the examples entering the upper and lower limits of integration.