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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (x^2+3)/(x^2-1)
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Integral of -x^-2
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Integral of dx/(2*x+7)
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Integral of 2*x/(x^2-5)
- Graphing y =:
- 2*x/(x^2-5)
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Identical expressions
- two *x/(x^ two - five)
- 2 multiply by x divide by (x squared minus 5)
- two multiply by x divide by (x to the power of two minus five)
- 2*x/(x2-5)
- 2*x/x2-5
- 2*x/(x²-5)
- 2*x/(x to the power of 2-5)
- 2x/(x^2-5)
- 2x/(x2-5)
- 2x/x2-5
- 2x/x^2-5
- 2*x divide by (x^2-5)
- 2*x/(x^2-5)dx
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Similar expressions
- 2*x/(x^2+5)
Integral of 2*x/(x^2-5) dx
The solution
You have entered
[src]
1 / | | 2*x | ------ dx | 2 | x - 5 | / 0
$$\int\limits_{0}^{1} \frac{2 x}{x^{2} - 5}\, dx$$
Integral((2*x)/(x^2 - 5), (x, 0, 1))
Detail solution
We have the integral:
/ | | 2*x | ------ dx | 2 | x - 5 | /
Rewrite the integrand
2*x 2*x ------ = ------------ 2 2 x - 5 x + 0*x - 5
or
/ | | 2*x | ------ dx | 2 = | x - 5 | /
/ | | 2*x | ------------ dx | 2 | x + 0*x - 5 | /
In the integral
/ | | 2*x | ------------ dx | 2 | x + 0*x - 5 | /
do replacement
2 u = x
then
the integral =
/ | | 1 | ------ du = log(-5 + u) | -5 + u | /
do backward replacement
/ | | 2*x / 2\ | ------------ dx = log\-5 + x / | 2 | x + 0*x - 5 | /
Solution is:
/ 2\ C + log\-5 + x /
The answer (Indefinite)
[src]
/ | | 2*x / 2\ | ------ dx = C + log\-5 + x / | 2 | x - 5 | /
$$\int \frac{2 x}{x^{2} - 5}\, dx = C + \log{\left(x^{2} - 5 \right)}$$
The graph
The answer
[src]
-log(5) + log(4)
$$- \log{\left(5 \right)} + \log{\left(4 \right)}$$
=
=
-log(5) + log(4)
$$- \log{\left(5 \right)} + \log{\left(4 \right)}$$
-log(5) + log(4)
The graph
Use the examples entering the upper and lower limits of integration.