三角関数の原始関数の一覧
∫ d x csc  x + 1 = x − 2 sin  x 2 cos  x 2 + sin  x 2 + C {\displaystyle \int {\frac {\mathrm {d} x}{\csc {x}+1}}=x-{\frac {2\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}+\sin {\frac {x}{2}}}}+C}
∫ d x csc  x − 1 = 2 sin  x 2 cos  x 2 − sin  x 2 − x + C {\displaystyle \int {\frac {\mathrm {d} x}{\csc {x}-1}}={\frac {2\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}-\sin {\frac {x}{2}}}}-x+C}