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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
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How to use it?
- Integral of d{x}:
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Integral of e^(4*x)*dx
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Integral of 1/(x^2-9)
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Integral of 2*x/(-1+x)
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Integral of 1/(2+3x^2)
- How do you in partial fractions?:
- 1/(x^2-9)
- Graphing y =:
- 1/(x^2-9)
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Identical expressions
- one /(x^ two - nine)
- 1 divide by (x squared minus 9)
- one divide by (x to the power of two minus nine)
- 1/(x2-9)
- 1/x2-9
- 1/(x²-9)
- 1/(x to the power of 2-9)
- 1/x^2-9
- 1 divide by (x^2-9)
- 1/(x^2-9)dx
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Similar expressions
- 1/(x^2+9)
Integral of 1/(x^2-9) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 2 | x - 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} - 9}\, dx$$
Integral(1/(x^2 - 9), (x, 0, 1))
Detail solution
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Add the constant of integration:
PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=-9, context=1/(x**2 - 9), symbol=x), False), (ArccothRule(a=1, b=1, c=-9, context=1/(x**2 - 9), symbol=x), x**2 > 9), (ArctanhRule(a=1, b=1, c=-9, context=1/(x**2 - 9), symbol=x), x**2 < 9)], context=1/(x**2 - 9), symbol=x)
The answer is:
The answer (Indefinite)
[src]
// /x\ \
||-acoth|-| |
/ || \3/ 2 |
| ||---------- for x > 9|
| 1 || 3 |
| ------ dx = C + |< |
| 2 || /x\ |
| x - 9 ||-atanh|-| |
| || \3/ 2 |
/ ||---------- for x < 9|
\\ 3 /
$$\int \frac{1}{x^{2} - 9}\, dx = C + \begin{cases} - \frac{\operatorname{acoth}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} > 9 \\- \frac{\operatorname{atanh}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} < 9 \end{cases}$$
The graph
The answer
[src]
log(4) log(2)
- ------ + ------
6 6
$$- \frac{\log{\left(4 \right)}}{6} + \frac{\log{\left(2 \right)}}{6}$$
=
=
log(4) log(2)
- ------ + ------
6 6
$$- \frac{\log{\left(4 \right)}}{6} + \frac{\log{\left(2 \right)}}{6}$$
-log(4)/6 + log(2)/6
The graph
Use the examples entering the upper and lower limits of integration.