Integrating Other Functions (Trig, ln & e etc) (CIE AS Maths: Pure 2)

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)

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  

• Remember
  • 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