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How to use it?
- Integral of d{x}:
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Integral of exp(7*x)*sin(x)
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Integral of sin(x)^2*cos(x)^4
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Integral of 1/(1+(x+1)^(1/3))
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Integral of x^3*ln(x)
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Identical expressions
- one /sqrt(two -x^(- two))
- 1 divide by square root of (2 minus x to the power of ( minus 2))
- one divide by square root of (two minus x to the power of ( minus two))
- 1/√(2-x^(-2))
- 1/sqrt(2-x(-2))
- 1/sqrt2-x-2
- 1/sqrt2-x^-2
- 1 divide by sqrt(2-x^(-2))
- 1/sqrt(2-x^(-2))dx
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Similar expressions
- 1/sqrt(2+x^(-2))
- 1/sqrt(2-x^(2))
Integral of 1/sqrt(2-x^(-2)) dx
The solution
You have entered
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1 / | | 1 | ------------- dx | ________ | / 1 | / 2 - -- | / 2 | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{2 - \frac{1}{x^{2}}}}\, dx$$
Integral(1/(sqrt(2 - 1/x^2)), (x, 0, 1))
The answer (Indefinite)
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// ___________ \
|| / 2 |
/ ||\/ -1 + 2*x | 2| |
| ||-------------- for 2*|x | > 1|
| 1 || 2 |
| ------------- dx = C + |< |
| ________ || __________ |
| / 1 || / 2 |
| / 2 - -- ||I*\/ 1 - 2*x |
| / 2 ||--------------- otherwise |
| \/ x \\ 2 /
|
/
$$\int \frac{1}{\sqrt{2 - \frac{1}{x^{2}}}}\, dx = C + \begin{cases} \frac{\sqrt{2 x^{2} - 1}}{2} & \text{for}\: 2 \left|{x^{2}}\right| > 1 \\\frac{i \sqrt{1 - 2 x^{2}}}{2} & \text{otherwise} \end{cases}$$
The graph
The answer
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1 / | | / x 2 | |-------------- for 2*x > 1 | | ___________ | | / 2 | |\/ -1 + 2*x | < dx | | -I*x | |------------- otherwise | | __________ | | / 2 | \\/ 1 - 2*x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{x}{\sqrt{2 x^{2} - 1}} & \text{for}\: 2 x^{2} > 1 \\- \frac{i x}{\sqrt{1 - 2 x^{2}}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / x 2 | |-------------- for 2*x > 1 | | ___________ | | / 2 | |\/ -1 + 2*x | < dx | | -I*x | |------------- otherwise | | __________ | | / 2 | \\/ 1 - 2*x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{x}{\sqrt{2 x^{2} - 1}} & \text{for}\: 2 x^{2} > 1 \\- \frac{i x}{\sqrt{1 - 2 x^{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((x/sqrt(-1 + 2*x^2), 2*x^2 > 1), (-i*x/sqrt(1 - 2*x^2), True)), (x, 0, 1))
Numerical answer
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(0.505674648770025 - 0.454284972789841j)
(0.505674648770025 - 0.454284972789841j)
Use the examples entering the upper and lower limits of integration.