不定积分的公式如下:
∫ a dx = ax + C,a和C都是常数;
∫ x^a dx = [x^(a + 1)]/(a + 1) + C,其中a为常数且 a ≠ -1;
∫ 1/x dx = ln|x| + C;
∫ a^x dx = (1/lna)a^x + C,其中a > 0 且 a ≠ 1;
∫ e^x dx = e^x + C;
∫ cosx dx = sinx + C;
∫ sinx dx = - cosx + C;
∫ cotx dx = ln|sinx| + C = - ln|cscx| + C;
∫ tanx dx = - ln|cosx| + C = ln|secx| + C;
∫ secx dx =ln|cot(x/2)| + C = (1/2)ln|(1 + sinx)/(1 - sinx)| + C = - ln|secx - tanx| + C = ln|secx + tanx| + C;
∫ cscx dx = ln|tan(x/2)| + C = (1/2)ln|(1 - cosx)/(1 + cosx)| + C = - ln|cscx + cotx| + C = ln|cscx - cotx| + C;
∫ sec^2(x) dx = tanx + C;
∫ csc^2(x) dx = - cotx + C;
∫ secxtanx dx = secx + C;
∫ cscxcotx dx = - cscx + C;
∫ dx/(a^2 + x^2) = (1/a)arctan(x/a) + C;
∫ dx/√(a^2 - x^2) = arcsin(x/a) + C;
∫ dx/√(x^2 + a^2) = ln|x + √(x^2 + a^2)| + C;
∫ dx/√(x^2 - a^2) = ln|x + √(x^2 - a^2)| + C;
∫ √(x^2 - a^2) dx = (x/2)√(x^2 - a^2) - (a^2/2)ln|x + √(x^2 - a^2)| + C;
∫ √(x^2 + a^2) dx = (x/2)√(x^2 + a^2) + (a^2/2)ln|x + √(x^2 + a^2)| + C;
∫ √(a^2 - x^2) dx = (x/2)√(a^2 - x^2) + (a^2/2)arcsin(x/a) + C;
若f(x)是F(x)的导函数(简称导数),则F(x)+C(C为任意常数)为f(x)的不定积分,f(x)的不定积分用符号表示为∫f(x)dx,即∫f(x)dx=F(x)+ C。