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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of ex^2
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Integral of 1-7*x^2
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Integral of xe^(1-x)
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Integral of -xe^x
- Derivative of:
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1/(x^2-3)
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Identical expressions
- one /(x^ two - three)
- 1 divide by (x squared minus 3)
- one divide by (x to the power of two minus three)
- 1/(x2-3)
- 1/x2-3
- 1/(x²-3)
- 1/(x to the power of 2-3)
- 1/x^2-3
- 1 divide by (x^2-3)
- 1/(x^2-3)dx
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Similar expressions
- 1/(x^2+3)
Integral of 1/(x^2-3) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 2 | x - 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} - 3}\, dx$$
Integral(1/(x^2 - 3), (x, 0, 1))
Detail solution
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Add the constant of integration:
PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), False), (ArccothRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), x**2 > 3), (ArctanhRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), x**2 < 3)], context=1/(x**2 - 3), symbol=x)
The answer is:
The answer (Indefinite)
[src]
// / ___\ \
|| ___ |x*\/ 3 | |
||-\/ 3 *acoth|-------| |
/ || \ 3 / 2 |
| ||---------------------- for x > 3|
| 1 || 3 |
| ------ dx = C + |< |
| 2 || / ___\ |
| x - 3 || ___ |x*\/ 3 | |
| ||-\/ 3 *atanh|-------| |
/ || \ 3 / 2 |
||---------------------- for x < 3|
\\ 3 /
$$\int \frac{1}{x^{2} - 3}\, dx = C + \begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} < 3 \end{cases}$$
The graph
The answer
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 /
- ------------------------- - -------------------- + ------------------------------ + ----------------
6 6 6 6
$$- \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6}$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\
\/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 /
- ------------------------- - -------------------- + ------------------------------ + ----------------
6 6 6 6
$$- \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6}$$
-sqrt(3)*(pi*i + log(sqrt(3)))/6 - sqrt(3)*log(1 + sqrt(3))/6 + sqrt(3)*(pi*i + log(-1 + sqrt(3)))/6 + sqrt(3)*log(sqrt(3))/6
The graph
Use the examples entering the upper and lower limits of integration.