Integrating Other Functions (Trig, ln & e etc) (CIE A Level Maths: Pure 3): Revision Note

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

Integrating  and 

• Recall that 
• Then  and