CIE A Level Maths: Pure 3复习笔记5.1.1 Integrating Other Functions (Trig, ln & e etc)

Isn’t integration just the reverse of differentiation?

• Yes, but remember “+c”, the constant of integration …
  • … unless finding a definite integral
• Recognising common results helps to make integration easier
• (See Differentiating Other Functions)
• You are given all the standard integrals in the formula booklet

How do I integrate exponentials/e^x? 

• The gradient of e^kx is ke^kx
  • ie y = e^kx, dy/dx = ke^kx
• The reverse applies when integrating
• This is an example of reverse chain rule

Integrating 1/x 

• Remember 1/x = x^-1
  • The method for integrating powers does not apply if the power is -1

Integrating sin and cos

• Note the minus in the integral of sin x
• The integral of tan x is ln|sec x| + c