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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
-
Integral of -2/x
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Integral of ctg(x)^4
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Integral of tg²xdx
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Integral of e^5*x*dx
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Identical expressions
- dx/(x^ two -10x+ twenty-nine)
- dx divide by (x squared minus 10x plus 29)
- dx divide by (x to the power of two minus 10x plus twenty minus nine)
- dx/(x2-10x+29)
- dx/x2-10x+29
- dx/(x²-10x+29)
- dx/(x to the power of 2-10x+29)
- dx/x^2-10x+29
- dx divide by (x^2-10x+29)
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Similar expressions
- dx/(x^2-10x-29)
- dx/(x^2+10x+29)
Integral of dx/(x^2-10x+29) dx
The solution
You have entered
[src]
1 / | | 1 | 1*-------------- dx | 2 | x - 10*x + 29 | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x^{2} - 10 x + 29}\, dx$$
Integral(1/(x^2 - 10*x + 29), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | 1*1*-------------- dx | 2 | x - 10*x + 29 | /
Rewrite the integrand
1 1
1*-------------- = ------------------
2 / 2 \
x - 10*x + 29 |/ x 5\ |
4*||- - + -| + 1|
\\ 2 2/ /or
/ | | 1 | 1*1*-------------- dx | 2 = | x - 10*x + 29 | /
/
|
| 1
| -------------- dx
| 2
| / x 5\
| |- - + -| + 1
| \ 2 2/
|
/
--------------------
4 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 5\
| |- - + -| + 1
| \ 2 2/
|
/
--------------------
4 do replacement
5 x
v = - - -
2 2then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
4 4 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 5\
| |- - + -| + 1
| \ 2 2/ / 5 x\
| atan|- - + -|
/ \ 2 2/
-------------------- = -------------
4 2 Solution is:
/ 5 x\
atan|- - + -|
\ 2 2/
C + -------------
2
The answer (Indefinite)
[src]
/ / 5 x\ | atan|- - + -| | 1 \ 2 2/ | 1*-------------- dx = C + ------------- | 2 2 | x - 10*x + 29 | /
$${{\arctan \left({{2\,x-10}\over{4}}\right)}\over{2}}$$
The graph
The answer
[src]
atan(5/2) atan(2)
--------- - -------
2 2
$${{\arctan \left({{5}\over{2}}\right)}\over{2}}-{{\arctan 2}\over{2
}}$$
=
=
atan(5/2) atan(2)
--------- - -------
2 2
$$- \frac{\operatorname{atan}{\left(2 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.