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