![special functions - Is anything known about $2\pi$ integer multiple arguments of the cosine integral? - Mathematics Stack Exchange special functions - Is anything known about $2\pi$ integer multiple arguments of the cosine integral? - Mathematics Stack Exchange](https://i.stack.imgur.com/a4NAc.jpg)
special functions - Is anything known about $2\pi$ integer multiple arguments of the cosine integral? - Mathematics Stack Exchange
![int ^ { pi / 2 } ( x - [ cos x ] ) d x = ) where ( [ t ] = ) greatest integer or equal to t ( boldsymbol { Q } boldsymbol { pi } ^ { 2 } ) ( frac { pi ^ { 2 } } { 8 } - frac { pi } { 8 } ) ( pi ^ { 2 } ) ( pi ) int ^ { pi / 2 } ( x - [ cos x ] ) d x = ) where ( [ t ] = ) greatest integer or equal to t ( boldsymbol { Q } boldsymbol { pi } ^ { 2 } ) ( frac { pi ^ { 2 } } { 8 } - frac { pi } { 8 } ) ( pi ^ { 2 } ) ( pi )](https://toppr-doubts-media.s3.amazonaws.com/images/2241938/ebd576c1-5a93-4a21-8641-5f5f1b22d329.jpg)
int ^ { pi / 2 } ( x - [ cos x ] ) d x = ) where ( [ t ] = ) greatest integer or equal to t ( boldsymbol { Q } boldsymbol { pi } ^ { 2 } ) ( frac { pi ^ { 2 } } { 8 } - frac { pi } { 8 } ) ( pi ^ { 2 } ) ( pi )
![trigonometry - Prove $\lceil z \rceil=z+\frac12-\frac{\tan^{-1}(\tan(\pi (z+0.5)))}{\pi}$ when $z$ is not an integer - Mathematics Stack Exchange trigonometry - Prove $\lceil z \rceil=z+\frac12-\frac{\tan^{-1}(\tan(\pi (z+0.5)))}{\pi}$ when $z$ is not an integer - Mathematics Stack Exchange](https://i.stack.imgur.com/uXjMU.jpg)