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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (ctgx)^2
- Integral of y-x
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Integral of xlgx
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Integral of sin30
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Identical expressions
- one /(twenty-five +4x^ two)
- 1 divide by (25 plus 4x squared )
- one divide by (twenty minus five plus 4x to the power of two)
- 1/(25+4x2)
- 1/25+4x2
- 1/(25+4x²)
- 1/(25+4x to the power of 2)
- 1/25+4x^2
- 1 divide by (25+4x^2)
- 1/(25+4x^2)dx
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Similar expressions
- 1/(25-4x^2)
Integral of 1/(25+4x^2) dx
The solution
You have entered
[src]
1 / | | 1 | --------- dx | 2 | 25 + 4*x | / 0
$$\int\limits_{0}^{1} \frac{1}{4 x^{2} + 25}\, dx$$
Integral(1/(25 + 4*x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | --------- dx | 2 | 25 + 4*x | /
Rewrite the integrand
1 1
--------- = ----------------
2 / 2 \
25 + 4*x |/-2*x\ |
25*||----| + 1|
\\ 5 / /or
/ | | 1 | --------- dx | 2 = | 25 + 4*x | /
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 5 /
|
/
-----------------
25 In the integral
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 5 /
|
/
-----------------
25 do replacement
-2*x
v = ----
5 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
25 25 do backward replacement
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 5 / /2*x\
| atan|---|
/ \ 5 /
----------------- = ---------
25 10 Solution is:
/2*x\
atan|---|
\ 5 /
C + ---------
10
The answer (Indefinite)
[src]
/ /2*x\ | atan|---| | 1 \ 5 / | --------- dx = C + --------- | 2 10 | 25 + 4*x | /
$$\int \frac{1}{4 x^{2} + 25}\, dx = C + \frac{\operatorname{atan}{\left(\frac{2 x}{5} \right)}}{10}$$
The graph
The answer
[src]
atan(2/5)
---------
10
$$\frac{\operatorname{atan}{\left(\frac{2}{5} \right)}}{10}$$
=
=
atan(2/5)
---------
10
$$\frac{\operatorname{atan}{\left(\frac{2}{5} \right)}}{10}$$
atan(2/5)/10
The graph
Use the examples entering the upper and lower limits of integration.