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 x/(sinx^2)^2
-
Integral of (sqrt(x)-2)^2/x
-
Integral of (sin(3x))^5
-
Integral of e^xsin(x/2)
-
Identical expressions
- (x+ one)/(x^ two +2x+ one)
- (x plus 1) divide by (x squared plus 2x plus 1)
- (x plus one) divide by (x to the power of two plus 2x plus one)
- (x+1)/(x2+2x+1)
- x+1/x2+2x+1
- (x+1)/(x²+2x+1)
- (x+1)/(x to the power of 2+2x+1)
- x+1/x^2+2x+1
- (x+1) divide by (x^2+2x+1)
- (x+1)/(x^2+2x+1)dx
-
Similar expressions
- (x-1)/(x^2+2x+1)
- (x+1)/(x^2+2x-1)
- (x+1)/(x^2-2x+1)
Integral of (x+1)/(x^2+2x+1) dx
The solution
You have entered
[src]
1 / | | x + 1 | ------------ dx | 2 | x + 2*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x + 1}{\left(x^{2} + 2 x\right) + 1}\, dx$$
Integral((x + 1)/(x^2 + 2*x + 1), (x, 0, 1))
Detail solution
We have the integral:
/ | | x + 1 | ------------ dx | 2 | x + 2*x + 1 | /
Rewrite the integrand
/ 2*x + 2 \
|------------|
| 2 |
x + 1 \x + 2*x + 1/
------------ = --------------
2 2
x + 2*x + 1 or
/ | | x + 1 | ------------ dx | 2 = | x + 2*x + 1 | /
/
|
| 2*x + 2
| ------------ dx
| 2
| x + 2*x + 1
|
/
------------------
2 In the integral
/
|
| 2*x + 2
| ------------ dx
| 2
| x + 2*x + 1
|
/
------------------
2 do replacement
2 u = x + 2*x
then
the integral =
/
|
| 1
| ----- du
| 1 + u
|
/ log(1 + u)
----------- = ----------
2 2 do backward replacement
/
|
| 2*x + 2
| ------------ dx
| 2
| x + 2*x + 1
|
/
------------------ = log(1 + x)
2 Solution is:
C + log(1 + x)
The answer (Indefinite)
[src]
/ | / 2 \ | x + 1 log\x + 2*x + 1/ | ------------ dx = C + ----------------- | 2 2 | x + 2*x + 1 | /
$$\int \frac{x + 1}{\left(x^{2} + 2 x\right) + 1}\, dx = C + \frac{\log{\left(\left(x^{2} + 2 x\right) + 1 \right)}}{2}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.