Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Logarithmic Integral
What is Logarithmic Integral?
The antiderivative of one over x, equal to the natural logarithm of the modulus of x plus an arbitrary constant. It is the single case the power rule for integration cannot handle, because raising the index minus one by one gives zero and the rule would require division by zero. The modulus signs are needed so that the antiderivative is valid on intervals where x is negative as well as where it is positive, since the natural logarithm itself is only defined for positive arguments. The related form one over a x plus b integrates to one over a times the natural logarithm of the modulus of a x plus b, plus a constant, provided a is not zero.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.