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- Improper integral
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-
How to use it?
- Integral of d{x}:
-
Integral of 1/(x^2+3)
-
Integral of x^-3
- Integral of a^x
-
Integral of dy/y^2
- Derivative of:
-
1/(x^2+25)
- How do you in partial fractions?:
- 1/(x^2+25)
- Graphing y =:
- 1/(x^2+25)
-
Identical expressions
- one /(x^ two + twenty-five)
- 1 divide by (x squared plus 25)
- one divide by (x to the power of two plus twenty minus five)
- 1/(x2+25)
- 1/x2+25
- 1/(x²+25)
- 1/(x to the power of 2+25)
- 1/x^2+25
- 1 divide by (x^2+25)
- 1/(x^2+25)dx
-
Similar expressions
- 1/(x^2-25)
Integral of 1/(x^2+25) dx
The solution
You have entered
[src]
1 / | | 1 | ------- dx | 2 | x + 25 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 25}\, dx$$
Integral(1/(x^2 + 25), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------- dx | 2 | x + 25 | /
Rewrite the integrand
1 1
------- = ---------------
2 / 2 \
x + 25 |/-x \ |
25*||---| + 1|
\\ 5 / /or
/ | | 1 | ------- dx | 2 = | x + 25 | /
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 5 /
|
/
----------------
25 In the integral
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 5 /
|
/
----------------
25 do replacement
-x
v = ---
5 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
25 25 do backward replacement
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 5 / /x\
| atan|-|
/ \5/
---------------- = -------
25 5 Solution is:
/x\
atan|-|
\5/
C + -------
5
The answer (Indefinite)
[src]
/ /x\ | atan|-| | 1 \5/ | ------- dx = C + ------- | 2 5 | x + 25 | /
$$\int \frac{1}{x^{2} + 25}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{5} \right)}}{5}$$
The graph
The answer
[src]
atan(1/5)
---------
5
$$\frac{\operatorname{atan}{\left(\frac{1}{5} \right)}}{5}$$
=
=
atan(1/5)
---------
5
$$\frac{\operatorname{atan}{\left(\frac{1}{5} \right)}}{5}$$
atan(1/5)/5
The graph
Use the examples entering the upper and lower limits of integration.