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How to use it?
- Integral of d{x}:
- Integral of |x-1|
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Integral of sin^2(x)cos^2(x)
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Integral of (3x-2)^2
- Integral of (1+log(x))/x
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Identical expressions
- one /(three x^ two -12x+3)
- 1 divide by (3x squared minus 12x plus 3)
- one divide by (three x to the power of two minus 12x plus 3)
- 1/(3x2-12x+3)
- 1/3x2-12x+3
- 1/(3x²-12x+3)
- 1/(3x to the power of 2-12x+3)
- 1/3x^2-12x+3
- 1 divide by (3x^2-12x+3)
- 1/(3x^2-12x+3)dx
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Similar expressions
- 1/(3x^2-12x-3)
- 1/(3x^2+12x+3)
Integral of 1/(3x^2-12x+3) dx
The solution
You have entered
[src]
1 / | | 1 | --------------- dx | 2 | 3*x - 12*x + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(3 x^{2} - 12 x\right) + 3}\, dx$$
Integral(1/(3*x^2 - 12*x + 3), (x, 0, 1))
The answer (Indefinite)
[src]
/ / ___ \
| ___ |\/ 3 *(-2 + x)|
|-\/ 3 *acoth|--------------|
| \ 3 / 2
|----------------------------- for (-2 + x) > 3
| 3
<
| / ___ \
| ___ |\/ 3 *(-2 + x)|
|-\/ 3 *atanh|--------------|
/ | \ 3 / 2
| |----------------------------- for (-2 + x) < 3
| 1 \ 3
| --------------- dx = C + -------------------------------------------------
| 2 3
| 3*x - 12*x + 3
|
/
$$\int \frac{1}{\left(3 x^{2} - 12 x\right) + 3}\, dx = C + \frac{\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3} \right)}}{3} & \text{for}\: \left(x - 2\right)^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3} \right)}}{3} & \text{for}\: \left(x - 2\right)^{2} < 3 \end{cases}}{3}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.