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How to use it?
- Integral of d{x}:
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Integral of (-1)/x^2
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Integral of 1/(x+2)^2
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Integral of x⁴
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Integral of x/(1+x²)
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Identical expressions
- (two x- five)/(x^2-5x+ four)
- (2x minus 5) divide by (x squared minus 5x plus 4)
- (two x minus five) divide by (x squared minus 5x plus four)
- (2x-5)/(x2-5x+4)
- 2x-5/x2-5x+4
- (2x-5)/(x²-5x+4)
- (2x-5)/(x to the power of 2-5x+4)
- 2x-5/x^2-5x+4
- (2x-5) divide by (x^2-5x+4)
- (2x-5)/(x^2-5x+4)dx
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Similar expressions
- (2x-5)/(x^2-5x-4)
- (2x-5)/(x^2+5x+4)
- (2x+5)/(x^2-5x+4)
- (2x-5)/((x^2-5x+4)^3)
Integral of (2x-5)/(x^2-5x+4) dx
The solution
You have entered
[src]
1 / | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 4 | / 0
$$\int\limits_{0}^{1} \frac{2 x - 5}{\left(x^{2} - 5 x\right) + 4}\, dx$$
Integral((2*x - 5)/(x^2 - 5*x + 4), (x, 0, 1))
Detail solution
We have the integral:
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 4 | /
Rewrite the integrand
True
or
/ | | 2*x - 5 | ------------ dx | 2 = | x - 5*x + 4 | /
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 4 | /
In the integral
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 4 | /
do replacement
2 u = x - 5*x
then
the integral =
/ | | 1 | ----- du = log(4 + u) | 4 + u | /
do backward replacement
/ | | 2*x - 5 / 2 \ | ------------ dx = log\4 + x - 5*x/ | 2 | x - 5*x + 4 | /
Solution is:
/ 2 \ C + log\4 + x - 5*x/
The answer (Indefinite)
[src]
/ | | 2*x - 5 / 2 \ | ------------ dx = C + log\x - 5*x + 4/ | 2 | x - 5*x + 4 | /
$$\int \frac{2 x - 5}{\left(x^{2} - 5 x\right) + 4}\, dx = C + \log{\left(\left(x^{2} - 5 x\right) + 4 \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.