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How to use it?
- Integral of d{x}:
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Integral of x/(raiz(2x-5))
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Integral of (x+1)/(x^2+2x-1)
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Integral of (x+1)/(2x²+3x-4)
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Integral of e^ydy
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Identical expressions
- (x+ one)/(x^ two +2x- one)
- (x plus 1) divide by (x squared plus 2x minus 1)
- (x plus one) divide by (x to the power of two plus 2x minus 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
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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
| / 2 \
/ log\-1 + x + 2*x/
------------------ = ------------------
2 2 Solution is:
/ 2 \
log\-1 + x + 2*x/
C + ------------------
2
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.