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How to use it?
- Integral of d{x}:
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Integral of k
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Integral of -y
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Integral of x*e^(2*x)*dx
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Integral of (1-x^2)^(1/2)
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Identical expressions
- (two *x- one)/(four *x^ two - four *x+ five)
- (2 multiply by x minus 1) divide by (4 multiply by x squared minus 4 multiply by x plus 5)
- (two multiply by x minus one) divide by (four multiply by x to the power of two minus four multiply by x plus five)
- (2*x-1)/(4*x2-4*x+5)
- 2*x-1/4*x2-4*x+5
- (2*x-1)/(4*x²-4*x+5)
- (2*x-1)/(4*x to the power of 2-4*x+5)
- (2x-1)/(4x^2-4x+5)
- (2x-1)/(4x2-4x+5)
- 2x-1/4x2-4x+5
- 2x-1/4x^2-4x+5
- (2*x-1) divide by (4*x^2-4*x+5)
- (2*x-1)/(4*x^2-4*x+5)dx
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Similar expressions
- (2*x-1)/(4*x^2+4*x+5)
- (2*x+1)/(4*x^2-4*x+5)
- (2*x-1)/(4*x^2-4*x-5)
Integral of (2*x-1)/(4*x^2-4*x+5) dx
The solution
You have entered
[src]
5 / | | 2*x - 1 | -------------- dx | 2 | 4*x - 4*x + 5 | / 0
$$\int\limits_{0}^{5} \frac{2 x - 1}{4 x^{2} - 4 x + 5}\, dx$$
Integral((2*x - 1*1)/(4*x^2 - 4*x + 5), (x, 0, 5))
Detail solution
We have the integral:
/ | | 2*x - 1 | 1*-------------- dx | 2 | 4*x - 4*x + 5 | /
Rewrite the integrand
/ 4*2*x - 4 \
|--------------| /0\
| 2 | |-|
2*x - 1 \4*x - 4*x + 5/ \4/
-------------- = ---------------- + ---------------
2 4 2
4*x - 4*x + 5 (-x + 1/2) + 1or
/ | | 2*x - 1 | 1*-------------- dx | 2 = | 4*x - 4*x + 5 | /
/
|
| 4*2*x - 4
| -------------- dx
| 2
| 4*x - 4*x + 5
|
/
--------------------
4 In the integral
/
|
| 4*2*x - 4
| -------------- dx
| 2
| 4*x - 4*x + 5
|
/
--------------------
4 do replacement
2 u = -4*x + 4*x
then
the integral =
/
|
| 1
| ----- du
| 5 + u
|
/ log(5 + u)
----------- = ----------
4 4 do backward replacement
/
|
| 4*2*x - 4
| -------------- dx
| 2
| 4*x - 4*x + 5
| / 2\
/ log\5 - 4*x + 4*x /
-------------------- = -------------------
4 4 In the integral
0
do replacement
v = 1/2 - x
then
the integral =
0 = 0
do backward replacement
0 = 0
Solution is:
/ 2\
log\5 - 4*x + 4*x /
C + -------------------
4
The answer (Indefinite)
[src]
/ | / 2\ | 2*x - 1 log\10 - 8*x + 8*x / | -------------- dx = C + -------------------- | 2 4 | 4*x - 4*x + 5 | /
$$\int \frac{2 x - 1}{4 x^{2} - 4 x + 5}\, dx = C + \frac{\log{\left(8 x^{2} - 8 x + 10 \right)}}{4}$$
The graph
The answer
[src]
log(5) log(85)
- ------ + -------
4 4
$$- \frac{\log{\left(5 \right)}}{4} + \frac{\log{\left(85 \right)}}{4}$$
=
=
log(5) log(85)
- ------ + -------
4 4
$$- \frac{\log{\left(5 \right)}}{4} + \frac{\log{\left(85 \right)}}{4}$$
The graph
Use the examples entering the upper and lower limits of integration.