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- 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 1/5x
-
Integral of x*dx/(x^2+1)
-
Integral of x^3*exp(x^2)
- Integral of x^2*a^x
- Derivative of:
-
(x-1)/(x^2+1)
- Graphing y =:
- (x-1)/(x^2+1)
- How do you in partial fractions?:
- (x-1)/(x^2+1)
-
Identical expressions
- (x- one)/(x^ two + one)
- (x minus 1) divide by (x squared plus 1)
- (x minus one) divide by (x to the power of two plus one)
- (x-1)/(x2+1)
- x-1/x2+1
- (x-1)/(x²+1)
- (x-1)/(x to the power of 2+1)
- x-1/x^2+1
- (x-1) divide by (x^2+1)
- (x-1)/(x^2+1)dx
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Similar expressions
- (x-1)/(x^2-1)
- (3x-1)/(x^2+10x+6)
- (x+1)/(x^2+1)
Integral of (x-1)/(x^2+1) dx
The solution
You have entered
[src]
1 / | | x - 1 | ------ dx | 2 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x - 1}{x^{2} + 1}\, dx$$
Integral((x - 1)/(x^2 + 1), (x, 0, 1))
Detail solution
We have the integral:
/ | | x - 1 | ------ dx | 2 | x + 1 | /
Rewrite the integrand
/ 2*x \
|------------| /-1 \
| 2 | |---|
x - 1 \x + 0*x + 1/ \ 1 /
------ = -------------- + ---------
2 2 2
x + 1 (-x) + 1or
/ | | x - 1 | ------ dx | 2 = | x + 1 | /
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 1 /
| |
/ | 1
------------------ - | --------- dx
2 | 2
| (-x) + 1
|
/ In the integral
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 1
|
/
------------------
2 do replacement
2 u = x
then
the integral =
/
|
| 1
| ----- du
| 1 + u
|
/ log(1 + u)
----------- = ----------
2 2 do backward replacement
/
|
| 2*x
| ------------ dx
| 2
| x + 0*x + 1
| / 2\
/ log\1 + x /
------------------ = -----------
2 2 In the integral
/ | | 1 - | --------- dx | 2 | (-x) + 1 | /
do replacement
v = -x
then
the integral =
/ | | 1 - | ------ dv = -atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 - | --------- dx = -atan(x) | 2 | (-x) + 1 | /
Solution is:
/ 2\
log\1 + x /
C + ----------- - atan(x)
2
The answer (Indefinite)
[src]
/ | / 2\ | x - 1 log\1 + x / | ------ dx = C + ----------- - atan(x) | 2 2 | x + 1 | /
$$\int \frac{x - 1}{x^{2} + 1}\, dx = C + \frac{\log{\left(x^{2} + 1 \right)}}{2} - \operatorname{atan}{\left(x \right)}$$
The graph
The answer
[src]
log(2) pi ------ - -- 2 4
$$- \frac{\pi}{4} + \frac{\log{\left(2 \right)}}{2}$$
=
=
log(2) pi ------ - -- 2 4
$$- \frac{\pi}{4} + \frac{\log{\left(2 \right)}}{2}$$
log(2)/2 - pi/4
The graph
Use the examples entering the upper and lower limits of integration.