Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Composite Linear Integral
What is Composite Linear Integral?
An integral in which the integrand is a standard function applied to a linear expression a x plus b. Because the derivative of a linear inside is the constant a, reversing the chain rule requires only division by that constant, so the antiderivative is the ordinary antiderivative of the standard function evaluated at a x plus b and then divided by a. This gives the standard forms for the power, sine, cosine, secant squared and exponential functions of a linear argument, each with a factor one over a and an arbitrary constant. The method is valid only when the inside is linear; a non-linear inside has a non-constant derivative that cannot be divided out in this way.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.