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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+4)
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Integral of (x+3)e^x
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Integral of sin³xcosx
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Integral of 1/(x^2+2x+10)
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Identical expressions
- one /(four + nine *x^ two)
- 1 divide by (4 plus 9 multiply by x squared )
- one divide by (four plus nine multiply by x to the power of two)
- 1/(4+9*x2)
- 1/4+9*x2
- 1/(4+9*x²)
- 1/(4+9*x to the power of 2)
- 1/(4+9x^2)
- 1/(4+9x2)
- 1/4+9x2
- 1/4+9x^2
- 1 divide by (4+9*x^2)
- 1/(4+9*x^2)dx
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Similar expressions
- 1/(4-9*x^2)
Integral of 1/(4+9*x^2) dx
The solution
You have entered
[src]
1 / | | 1 | -------- dx | 2 | 4 + 9*x | / 0
$$\int\limits_{0}^{1} \frac{1}{9 x^{2} + 4}\, dx$$
Integral(1/(4 + 9*x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | -------- dx | 2 | 4 + 9*x | /
Rewrite the integrand
1 1
-------- = ---------------
2 / 2 \
4 + 9*x |/-3*x\ |
4*||----| + 1|
\\ 2 / /or
/ | | 1 | -------- dx | 2 = | 4 + 9*x | /
/
|
| 1
| ----------- dx
| 2
| /-3*x\
| |----| + 1
| \ 2 /
|
/
-----------------
4 In the integral
/
|
| 1
| ----------- dx
| 2
| /-3*x\
| |----| + 1
| \ 2 /
|
/
-----------------
4 do replacement
-3*x
v = ----
2 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
4 4 do backward replacement
/
|
| 1
| ----------- dx
| 2
| /-3*x\
| |----| + 1
| \ 2 / /3*x\
| atan|---|
/ \ 2 /
----------------- = ---------
4 6 Solution is:
/3*x\
atan|---|
\ 2 /
C + ---------
6
The answer (Indefinite)
[src]
/ /3*x\ | atan|---| | 1 \ 2 / | -------- dx = C + --------- | 2 6 | 4 + 9*x | /
$$\int \frac{1}{9 x^{2} + 4}\, dx = C + \frac{\operatorname{atan}{\left(\frac{3 x}{2} \right)}}{6}$$
The graph
The answer
[src]
atan(3/2)
---------
6
$$\frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{6}$$
=
=
atan(3/2)
---------
6
$$\frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{6}$$
atan(3/2)/6
Use the examples entering the upper and lower limits of integration.