فيما يلي قائمة لتكاملات التوابع غير المنطقة.
بفرض أن ( x 2 > a 2 ) {\displaystyle (x^{2}>a^{2})} ، من أجل ( x 2 < a 2 ) {\displaystyle (x^{2}<a^{2})} ، انظر المقطع اللاحق:
لاحظ أن ln | x + s a | = s g n ( x ) cosh − 1 | x a | = 1 2 ln ( x + s x − s ) {\displaystyle \ln \left|{\frac {x+s}{a}\right|=\mathrm {sgn} (x)\cosh ^{-1}\left|{\frac {x}{a}\right|={\frac {1}{2}\ln \left({\frac {x+s}{x-s}\right)} ،
حيث يجب أخذ القيمة الإيجابية لـ cosh − 1 | x a | {\displaystyle \cosh ^{-1}\left|{\frac {x}{a}\right|} .
، من أجل 
، انظر المقطع اللاحق:
،
.
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