Integrating Other Functions (Edexcel IAL Maths)

Integrating Other Functions (Trig, ln & e etc)

Spec point — 5.1

Integrating other functions

Is integration 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 e^x and e^kx?

• 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

How do I integrating 1/x?

• Remember $\frac{1}{x}=x^{-1}$

  • The method for integrating powers does not apply if the power is -1

How do I integrating sin x and cos x?

• Note the minus in the integral of sin x

How do I integrate tan x?

• The integral of tan x is ln|sec x| + c

Exam Hint

• Make sure you have a copy of the formula booklet during revision but don't try to remember everything in the formula booklet.
• However, do be familiar with the layout of the formula booklet – you’ll be able to locate quickly whatever you are after, and you do not want to be searching every line of every page!
• For formulae you think you have remembered, use the booklet to double-check.

Worked Example