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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^3*exp(x^2)
- Integral of x^2*a^x
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Integral of sec³x
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Integral of x*3^x
- Derivative of:
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atan(1/(x-1))
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Identical expressions
- atan(one /(x- one))
- arc tangent of gent of (1 divide by (x minus 1))
- arc tangent of gent of (one divide by (x minus one))
- atan1/x-1
- atan(1 divide by (x-1))
- atan(1/(x-1))dx
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Similar expressions
- atan(1/(x+1))
- arctan(1/(x-1))
Integral of atan(1/(x-1)) dx
The solution
You have entered
[src]
1 / | | / 1 \ | atan|-----| dx | \x - 1/ | / 0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx$$
Integral(atan(1/(x - 1)), (x, 0, 1))
The answer (Indefinite)
[src]
/ 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) pi
- ------ - --
2 4
$$- \frac{\pi}{4} - \frac{\log{\left(2 \right)}}{2}$$
=
=
log(2) pi
- ------ - --
2 4
$$- \frac{\pi}{4} - \frac{\log{\left(2 \right)}}{2}$$
-log(2)/2 - pi/4
Use the examples entering the upper and lower limits of integration.