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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x*sin(x)^2
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Integral of 1/(x^2+2x+10)
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Integral of (x+5)×sin3x
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Integral of (x^5-5.2x^3+5.5x^2-7x-3.5)/(x-1.245)
- Derivative of:
- 1/(x^2+2x+3)
- Graphing y =:
- 1/(x^2+2x+3)
-
Identical expressions
- one /(x^ two +2x+ three)
- 1 divide by (x squared plus 2x plus 3)
- one divide by (x to the power of two plus 2x plus three)
- 1/(x2+2x+3)
- 1/x2+2x+3
- 1/(x²+2x+3)
- 1/(x to the power of 2+2x+3)
- 1/x^2+2x+3
- 1 divide by (x^2+2x+3)
- 1/(x^2+2x+3)dx
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Similar expressions
- 1/(x^2-2x+3)
- 1/(x^2+2x-3)
Integral of 1/(x^2+2x+3) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 2 | x + 2*x + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 2 x\right) + 3}\, dx$$
Integral(1/(x^2 + 2*x + 3), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------------ dx | 2 | x + 2*x + 3 | /
Rewrite the integrand
1 1
------------ = ----------------------------
2 / 2 \
x + 2*x + 3 |/ ___ ___\ |
||-\/ 2 \/ 2 | |
2*||-------*x - -----| + 1|
\\ 2 2 / /or
/ | | 1 | ------------ dx | 2 = | x + 2*x + 3 | /
/
|
| 1
| ------------------------ dx
| 2
| / ___ ___\
| |-\/ 2 \/ 2 |
| |-------*x - -----| + 1
| \ 2 2 /
|
/
------------------------------
2 In the integral
/
|
| 1
| ------------------------ dx
| 2
| / ___ ___\
| |-\/ 2 \/ 2 |
| |-------*x - -----| + 1
| \ 2 2 /
|
/
------------------------------
2 do replacement
___ ___
\/ 2 x*\/ 2
v = - ----- - -------
2 2 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
2 2 do backward replacement
/
|
| 1
| ------------------------ dx
| 2
| / ___ ___\
| |-\/ 2 \/ 2 |
| |-------*x - -----| + 1 / ___ ___\
| \ 2 2 / ___ |\/ 2 x*\/ 2 |
| \/ 2 *atan|----- + -------|
/ \ 2 2 /
------------------------------ = ---------------------------
2 2 Solution is:
/ ___ ___\
___ |\/ 2 x*\/ 2 |
\/ 2 *atan|----- + -------|
\ 2 2 /
C + ---------------------------
2
The answer (Indefinite)
[src]
/ ___ \ / ___ |\/ 2 *(1 + x)| | \/ 2 *atan|-------------| | 1 \ 2 / | ------------ dx = C + ------------------------- | 2 2 | x + 2*x + 3 | /
$$\int \frac{1}{\left(x^{2} + 2 x\right) + 3}\, dx = C + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(x + 1\right)}{2} \right)}}{2}$$
The graph
The answer
[src]
/ ___\
___ |\/ 2 |
___ / ___\ \/ 2 *atan|-----|
\/ 2 *atan\\/ 2 / \ 2 /
----------------- - -----------------
2 2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \right)}}{2}$$
=
=
/ ___\
___ |\/ 2 |
___ / ___\ \/ 2 *atan|-----|
\/ 2 *atan\\/ 2 / \ 2 /
----------------- - -----------------
2 2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \right)}}{2}$$
sqrt(2)*atan(sqrt(2))/2 - sqrt(2)*atan(sqrt(2)/2)/2
The graph
Use the examples entering the upper and lower limits of integration.