As with other problems in integration the results in this revision note may have further uses such as

• evaluating a definite integral
• finding the constant of integration
• finding areas under a curve, between a line and a curve or between two curves

cosec?(cosecant, csc),?sec?(secant)?and?cot?(cotangent)?are the reciprocal functions of sine, cosine and tangent respectively.

What are the antiderivatives involving reciprocal trigonometric functions?

• These are?not?given in the?formula?booklet?directly
  • they are listed the other way round as ‘standard derivatives’
  • be careful with the negatives in the last two results
  • and remember “+c” !

How do I integrate these if a?linear?function of x is involved?

• All integration rules could apply alongside the results above
• The use of reverse chain rule is particularly common
  • For linear functions the following results can be usefulThese are not?in the formula booklet
  • • they can be deduced by spotting reverse chain rule
    • they are not essential to remember but can make problems easier

arcsin,?arccos?and?arctan?are (one-to-one) functions defined as the inverse functions of sine, cosine and tangent respectively.

What are the antiderivatives involving the inverse trigonometric functions?

How do I integrate these expressions if the denominator is not in the correct form?

What are the antiderivatives of exponential and logarithmic functions?

• How do I integrate exponentials and logarithms with a linear?function of x involved?
• These are not?in the formula booklet but can be derived using ‘adjust and compensate’ from?reverse?chain?rule

• Exam Tip