Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of (x+1)/(2x²+3x-4)
- Integral of ln|secx+tanx|dx
-
Integral of dx/(4*x^2+9)
-
Integral of dx/(4*x^2+4*x+2)
-
Identical expressions
- dx/(four *x^ two + nine)
- dx divide by (4 multiply by x squared plus 9)
- dx divide by (four multiply by x to the power of two plus nine)
- dx/(4*x2+9)
- dx/4*x2+9
- dx/(4*x²+9)
- dx/(4*x to the power of 2+9)
- dx/(4x^2+9)
- dx/(4x2+9)
- dx/4x2+9
- dx/4x^2+9
- dx divide by (4*x^2+9)
-
Similar expressions
- dx/(4*x^2-9)
Integral of dx/(4*x^2+9) dx
The solution
You have entered
[src]
1 / | | 1 | -------- dx | 2 | 4*x + 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{4 x^{2} + 9}\, dx$$
Integral(1/(4*x^2 + 9), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | -------- dx | 2 | 4*x + 9 | /
Rewrite the integrand
1 1
-------- = ---------------
2 / 2 \
4*x + 9 |/-2*x\ |
9*||----| + 1|
\\ 3 / /or
/ | | 1 | -------- dx | 2 = | 4*x + 9 | /
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 3 /
|
/
-----------------
9 In the integral
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 3 /
|
/
-----------------
9 do replacement
-2*x
v = ----
3 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
9 9 do backward replacement
/
|
| 1
| ----------- dx
| 2
| /-2*x\
| |----| + 1
| \ 3 / /2*x\
| atan|---|
/ \ 3 /
----------------- = ---------
9 6 Solution is:
/2*x\
atan|---|
\ 3 /
C + ---------
6
The answer (Indefinite)
[src]
/ /2*x\ | atan|---| | 1 \ 3 / | -------- dx = C + --------- | 2 6 | 4*x + 9 | /
$$\int \frac{1}{4 x^{2} + 9}\, dx = C + \frac{\operatorname{atan}{\left(\frac{2 x}{3} \right)}}{6}$$
The graph
The answer
[src]
atan(2/3)
---------
6
$$\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{6}$$
=
=
atan(2/3)
---------
6
$$\frac{\operatorname{atan}{\left(\frac{2}{3} \right)}}{6}$$
atan(2/3)/6
The graph
Use the examples entering the upper and lower limits of integration.