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