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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of (x^2-x+1)/(x^2+x+1)^2
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Integral of x/(1+sqrt(x))
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Integral of x/(1+3*x^2)
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Integral of tan^3xdx
- Graphing y =:
- x/(1+3*x^2)
- Limit of the function:
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x/(1+3*x^2)
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Identical expressions
- x/(one + three *x^ two)
- x divide by (1 plus 3 multiply by x squared )
- x divide by (one plus three multiply by x to the power of two)
- x/(1+3*x2)
- x/1+3*x2
- x/(1+3*x²)
- x/(1+3*x to the power of 2)
- x/(1+3x^2)
- x/(1+3x2)
- x/1+3x2
- x/1+3x^2
- x divide by (1+3*x^2)
- x/(1+3*x^2)dx
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Similar expressions
- x/(1-3*x^2)
Integral of x/(1+3*x^2) dx
The solution
You have entered
[src]
1 / | | x | -------- dx | 2 | 1 + 3*x | / 0
$$\int\limits_{0}^{1} \frac{x}{3 x^{2} + 1}\, dx$$
Integral(x/(1 + 3*x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | -------- dx | 2 | 1 + 3*x | /
Rewrite the integrand
/ 3*2*x \
|--------------| /0\
| 2 | |-|
x \3*x + 0*x + 1/ \1/
-------- = ---------------- + ---------------
2 6 2
1 + 3*x / ___ \
\-\/ 3 *x/ + 1or
/ | | x | -------- dx | 2 = | 1 + 3*x | /
/
|
| 3*2*x
| -------------- dx
| 2
| 3*x + 0*x + 1
|
/
--------------------
6 In the integral
/
|
| 3*2*x
| -------------- dx
| 2
| 3*x + 0*x + 1
|
/
--------------------
6 do replacement
2 u = 3*x
then
the integral =
/
|
| 1
| ----- du
| 1 + u
|
/ log(1 + u)
----------- = ----------
6 6 do backward replacement
/
|
| 3*2*x
| -------------- dx
| 2
| 3*x + 0*x + 1
| / 2\
/ log\1 + 3*x /
-------------------- = -------------
6 6 In the integral
0
do replacement
___ v = -x*\/ 3
then
the integral =
True
do backward replacement
True
Solution is:
/ 2\
log\1 + 3*x /
C + -------------
6
The answer (Indefinite)
[src]
/ | / 2\ | x log\1 + 3*x / | -------- dx = C + ------------- | 2 6 | 1 + 3*x | /
$$\int \frac{x}{3 x^{2} + 1}\, dx = C + \frac{\log{\left(3 x^{2} + 1 \right)}}{6}$$
The graph
The answer
[src]
log(4) ------ 6
$$\frac{\log{\left(4 \right)}}{6}$$
=
=
log(4) ------ 6
$$\frac{\log{\left(4 \right)}}{6}$$
log(4)/6
The graph
Use the examples entering the upper and lower limits of integration.