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