Grundintegrale
Integral(dx) = x + CIntegral(dx / x) = ln(c * x) = ln |x| + C
Integral(e^x * dx) = e^x + C
Integral(a^x * dx) = a^x/ln(a) + C = a^x * log(a, e) + C mit 0 < a != 1
Integral(cos(x) * dx) = sin(x) + C
Integral(sin(x) * dx) = - cos(x) + C
Integral(dx/cos^2x) = tan(x) + C
Integral(dx/sin^2x) = - cot(x) + C
Integral(cosh(x) * dx) = sinh(x) + C
Integral(sinh(x) * dx) = cosh(x) + C
Integral(dx / cosh^2x) = tanh(x) + C
Integral(dx / sinh^2x) = -coth(x) + C
Integral(dx / sqrt(1-x^2)) = arcsin(x) + C = - arccos(x) + C', wenn |x| < 1
Integral(dx / (1 + x^2)) = arctan(x) + C = -arccot(x) + C'
Integral(dx / sqrt(1 + x^2)) = arcsinh(x) + C = ln | x + sqrt(1 + x^2 | + C
Integral(dx / +-sqrt(x^2 - 1)) = arcosh|x| + C = ln | x +- sqrt(x^2 - 1) + C, wenn |x| > 1
Integral(dx/(1-x^2)) = artanh(x) + C = ln(sqrt((1+x) / (1-x))) + C, wenn |x| < 1
Integral(dx/(1-x^2)) = arcoth(x) + C1 = ln(sqrt((x+1) / (x-1))) + C1', wenn |x| > 1
