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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^e
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Integral of √(x+4)
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Integral of sin(2x)cos(2x)
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Integral of cos2
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Identical expressions
- arctan(one /(x- one))
- arc tangent of (1 divide by (x minus 1))
- arc tangent of (one divide by (x minus one))
- arctan1/x-1
- arctan(1 divide by (x-1))
- arctan(1/(x-1))dx
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Similar expressions
- arctan(1/(x+1))
Integral of arctan(1/(x-1)) dx
The solution
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2 / | | / 1 \ | atan|-----| dx | \x - 1/ | / -2
$$\int\limits_{-2}^{2} \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx$$
Integral(atan(1/(x - 1)), (x, -2, 2))
The answer (Indefinite)
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/ 2 \ / 2 \ / log|2 + --------| log|--------| | | 2| | 2| | / 1 \ \ (x - 1) / \(x - 1) / / 1 \ | atan|-----| dx = C + ----------------- - ------------- + (x - 1)*atan|-----| | \x - 1/ 2 2 \x - 1/ | /
$$\int \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx = C + \left(x - 1\right) \operatorname{atan}{\left(\frac{1}{x - 1} \right)} + \frac{\log{\left(2 + \frac{2}{\left(x - 1\right)^{2}} \right)}}{2} - \frac{\log{\left(\frac{2}{\left(x - 1\right)^{2}} \right)}}{2}$$
The graph
The answer
[src]
log(2) log(10) pi ------ - 3*atan(1/3) - ------- + -- 2 2 4
$$- \frac{\log{\left(10 \right)}}{2} - 3 \operatorname{atan}{\left(\frac{1}{3} \right)} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
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log(2) log(10) pi ------ - 3*atan(1/3) - ------- + -- 2 2 4
$$- \frac{\log{\left(10 \right)}}{2} - 3 \operatorname{atan}{\left(\frac{1}{3} \right)} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
log(2)/2 - 3*atan(1/3) - log(10)/2 + pi/4
Use the examples entering the upper and lower limits of integration.