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- Improper integral
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How to use it?
- Integral of d{x}:
-
Integral of cotx
- Integral of xlnxdx
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Integral of tan⁵x
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Integral of ln2x
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Identical expressions
- x/(eight - five *x^ two)
- x divide by (8 minus 5 multiply by x squared )
- x divide by (eight minus five multiply by x to the power of two)
- x/(8-5*x2)
- x/8-5*x2
- x/(8-5*x²)
- x/(8-5*x to the power of 2)
- x/(8-5x^2)
- x/(8-5x2)
- x/8-5x2
- x/8-5x^2
- x divide by (8-5*x^2)
- x/(8-5*x^2)dx
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Similar expressions
- x/(8+5*x^2)
Integral of x/(8-5*x^2) dx
The solution
You have entered
[src]
0 / | | x | -------- dx | 2 | 8 - 5*x | / 0
$$\int\limits_{0}^{0} \frac{x}{- 5 x^{2} + 8}\, dx$$
Integral(x/(8 - 5*x^2), (x, 0, 0))
Detail solution
We have the integral:
/ | | x | 1*-------- dx | 2 | 8 - 5*x | /
Rewrite the integrand
-5*2*x + 0
- ----------------
2
x - 5*x + 0*x + 8
-------- = -------------------
2 10
8 - 5*x or
/ | | x | 1*-------- dx | 2 = | 8 - 5*x | /
/
|
| -5*2*x + 0
- | ---------------- dx
| 2
| - 5*x + 0*x + 8
|
/
------------------------
10 In the integral
/
|
| -5*2*x + 0
- | ---------------- dx
| 2
| - 5*x + 0*x + 8
|
/
------------------------
10 do replacement
2 u = -5*x
then
the integral =
/
|
| 1
- | ----- du
| 8 + u
|
/ -log(8 + u)
------------- = ------------
10 10 do backward replacement
/
|
| -5*2*x + 0
- | ---------------- dx
| 2
| - 5*x + 0*x + 8
| / 2\
/ -log\-8 + 5*x /
------------------------ = ----------------
10 10 Solution is:
/ 2\
log\-8 + 5*x /
C - --------------
10
The answer (Indefinite)
[src]
/ | / 2\ | x log\8 - 5*x / | -------- dx = C - ------------- | 2 10 | 8 - 5*x | /
$$-{{\log \left(8-5\,x^2\right)}\over{10}}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.