Integral of arctan(1/(x-1)) dx
The solution
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/
|
/
$$\int \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx = C + \left(x - 1\right) \operatorname{atan}{\left(\frac{1}{x - 1} \right)} + \frac{\log{\left(2 + \frac{2}{\left(x - 1\right)^{2}} \right)}}{2} - \frac{\log{\left(\frac{2}{\left(x - 1\right)^{2}} \right)}}{2}$$
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) 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.