原始関数の一覧
∫ a 2 + x 2 d x = 1 2 x a 2 + x 2 + 1 2 a 2 ln  ( x + a 2 + x 2 ) + C {\displaystyle \int {\sqrt {a^{2}+x^{2}}}\,dx={\frac {1}{2}}x{\sqrt {a^{2}+x^{2}}}+{\frac {1}{2}}a^{2}\ln \left(x+{\sqrt {a^{2}+x^{2}}}\right)+C}
∫ x 2 a 2 + x 2 d x = 1 8 x ( a 2 + 2 x 2 ) a 2 + x 2 − 1 8 a 4 ln  ( x + a 2 + x 2 ) + C {\displaystyle \int x^{2}{\sqrt {a^{2}+x^{2}}}\,dx={\frac {1}{8}}x(a^{2}+2x^{2}){\sqrt {a^{2}+x^{2}}}-{\frac {1}{8}}a^{4}\ln \left(x+{\sqrt {a^{2}+x^{2}}}\right)+C}
∫ ( a x 2 + b x + c ) d x = a x 3 3 + b x 2 2 + c x + C {\displaystyle \int (ax^{2}+bx+c)\,dx={\frac {ax^{3}}{3}}+{\frac {bx^{2}}{2}}+cx+C}