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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(x^2+3)
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Integral of x^-3
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Integral of dx/1-cosx
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Integral of -4*x*exp(-2*x)
- Graphing y =:
- 1/(x^2+3)
- Derivative of:
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1/(x^2+3)
- Equation:
- 1/(x^2+3)
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Identical expressions
- one /(x^ two + three)
- 1 divide by (x squared plus 3)
- one divide by (x to the power of two plus three)
- 1/(x2+3)
- 1/x2+3
- 1/(x²+3)
- 1/(x to the power of 2+3)
- 1/x^2+3
- 1 divide by (x^2+3)
- 1/(x^2+3)dx
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Similar expressions
- 1/(x^2-3)
Integral of 1/(x^2+3) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 2 | x + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 3}\, dx$$
Integral(1/(x^2 + 3), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------ dx | 2 | x + 3 | /
Rewrite the integrand
1 1
------ = --------------------
2 / 2 \
x + 3 |/ ___ \ |
||-\/ 3 | |
3*||-------*x| + 1|
\\ 3 / /or
/ | | 1 | ------ dx | 2 = | x + 3 | /
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 3 |
| |-------*x| + 1
| \ 3 /
|
/
----------------------
3 In the integral
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 3 |
| |-------*x| + 1
| \ 3 /
|
/
----------------------
3 do replacement
___
-x*\/ 3
v = ---------
3 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
3 3 do backward replacement
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 3 |
| |-------*x| + 1 / ___\
| \ 3 / ___ |x*\/ 3 |
| \/ 3 *atan|-------|
/ \ 3 /
---------------------- = -------------------
3 3 Solution is:
/ ___\
___ |x*\/ 3 |
\/ 3 *atan|-------|
\ 3 /
C + -------------------
3
The answer (Indefinite)
[src]
/ ___\ / ___ |x*\/ 3 | | \/ 3 *atan|-------| | 1 \ 3 / | ------ dx = C + ------------------- | 2 3 | x + 3 | /
$$\int \frac{1}{x^{2} + 3}\, dx = C + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{3}$$
The graph
The answer
[src]
___ pi*\/ 3 -------- 18
$$\frac{\sqrt{3} \pi}{18}$$
=
=
___ pi*\/ 3 -------- 18
$$\frac{\sqrt{3} \pi}{18}$$
pi*sqrt(3)/18
The graph
Use the examples entering the upper and lower limits of integration.