Tích phân bất định
Tích phân xác định
Chú ý: bài này quy ước x>0.
Assume ( x 2 > a 2 ) {\displaystyle (x^{2}>a^{2})} , for ( x 2 < a 2 ) {\displaystyle (x^{2}<a^{2})} , see next section:
Note that ln | x + s a | = s g n ( x ) arcosh | x a | = 1 2 ln ( x + s x − s ) {\displaystyle \ln \left|{\frac {x+s}{a}}\right|=\mathrm {sgn} (x)\,\operatorname {arcosh} \left|{\frac {x}{a}}\right|={\frac {1}{2}}\ln \left({\frac {x+s}{x-s}}\right)} , where the positive value of arcosh | x a | {\displaystyle \operatorname {arcosh} \left|{\frac {x}{a}}\right|} is to be taken.
Tích phân hàm hợp (Integrals involving) R = a x 2 + b x + c {\displaystyle R={\sqrt {ax^{2}+bx+c}}}
Assume (ax2 + bx + c) cannot be reduced to the following expression (px + q)2 for some p and q.