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How to use it?
- Integral of d{x}:
-
Integral of √xdx
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Integral of √(1-x^2)
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Integral of 1/(2x)
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Integral of (e^x)/x
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Identical expressions
- x/(4x^ two - one)
- x divide by (4x squared minus 1)
- x divide by (4x to the power of two minus one)
- x/(4x2-1)
- x/4x2-1
- x/(4x²-1)
- x/(4x to the power of 2-1)
- x/4x^2-1
- x divide by (4x^2-1)
- x/(4x^2-1)dx
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Similar expressions
- x/(4x^2+1)
Integral of x/(4x^2-1) dx
The solution
You have entered
[src]
oo / | | x | -------- dx | 2 | 4*x - 1 | / 2
$$\int\limits_{2}^{\infty} \frac{x}{4 x^{2} - 1}\, dx$$
Integral(x/(4*x^2 - 1), (x, 2, oo))
Detail solution
We have the integral:
/ | | x | -------- dx | 2 | 4*x - 1 | /
Rewrite the integrand
/ 4*2*x \
|--------------|
| 2 |
x \4*x + 0*x - 1/
-------- = ----------------
2 8
4*x - 1 or
/ | | x | -------- dx | 2 = | 4*x - 1 | /
/
|
| 4*2*x
| -------------- dx
| 2
| 4*x + 0*x - 1
|
/
--------------------
8 In the integral
/
|
| 4*2*x
| -------------- dx
| 2
| 4*x + 0*x - 1
|
/
--------------------
8 do replacement
2 u = 4*x
then
the integral =
/
|
| 1
| ------ du
| -1 + u
|
/ log(-1 + u)
------------ = -----------
8 8 do backward replacement
/
|
| 4*2*x
| -------------- dx
| 2
| 4*x + 0*x - 1
| / 2\
/ log\-1 + 4*x /
-------------------- = --------------
8 8 Solution is:
/ 2\
log\-1 + 4*x /
C + --------------
8
The answer (Indefinite)
[src]
/ | / 2\ | x log\-1 + 4*x / | -------- dx = C + -------------- | 2 8 | 4*x - 1 | /
$$\int \frac{x}{4 x^{2} - 1}\, dx = C + \frac{\log{\left(4 x^{2} - 1 \right)}}{8}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.