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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^3+1)^1/2
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Integral of x/(16x^4+1)
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Integral of dx/(2*x+7)
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Integral of (2x-8)/(1-2x-x^2)
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Identical expressions
- (two x- eight)/(one -2x-x^2)
- (2x minus 8) divide by (1 minus 2x minus x squared )
- (two x minus eight) divide by (one minus 2x minus x squared )
- (2x-8)/(1-2x-x2)
- 2x-8/1-2x-x2
- (2x-8)/(1-2x-x²)
- (2x-8)/(1-2x-x to the power of 2)
- 2x-8/1-2x-x^2
- (2x-8) divide by (1-2x-x^2)
- (2x-8)/(1-2x-x^2)dx
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Similar expressions
- (2x-8)/(1+2x-x^2)
- (2x+8)/(1-2x-x^2)
- (2x-8)/(1-2x+x^2)
Integral of (2x-8)/(1-2x-x^2) dx
The solution
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[src]
1 / | | 2*x - 8 | ------------ dx | 2 | 1 - 2*x - x | / 0
$$\int\limits_{0}^{1} \frac{2 x - 8}{- x^{2} + \left(1 - 2 x\right)}\, dx$$
Integral((2*x - 8)/(1 - 2*x - x^2), (x, 0, 1))
The answer (Indefinite)
[src]
// / ___ \ \
|| ___ |\/ 2 *(1 + x)| |
||-\/ 2 *acoth|-------------| |
/ || \ 2 / 2 |
| ||---------------------------- for (1 + x) > 2|
| 2*x - 8 / 2 \ || 2 |
| ------------ dx = C - log\-1 + x + 2*x/ + 10*|< |
| 2 || / ___ \ |
| 1 - 2*x - x || ___ |\/ 2 *(1 + x)| |
| ||-\/ 2 *atanh|-------------| |
/ || \ 2 / 2 |
||---------------------------- for (1 + x) < 2|
\\ 2 /
$$\int \frac{2 x - 8}{- x^{2} + \left(1 - 2 x\right)}\, dx = C + 10 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x + 1\right)}{2} \right)}}{2} & \text{for}\: \left(x + 1\right)^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x + 1\right)}{2} \right)}}{2} & \text{for}\: \left(x + 1\right)^{2} < 2 \end{cases}\right) - \log{\left(x^{2} + 2 x - 1 \right)}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.