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