4 Integration using partial fractions
Sometimes expressions which at first sight look impossible to integrate using the techniques already met may in fact be integrated by first expressing them as simpler partial fractions, and then using the techniques described earlier in this Section. Consider the following Task.
Task!
Express [maths rendering] as the sum of its partial fractions.
Hence find [maths rendering]
First produce the partial fractions. Write the fraction in the form [maths rendering] and find [maths rendering] .
[maths rendering] , [maths rendering] Now integrate each term separately:
[maths rendering]
Exercises
By expressing the following in partial fractions, evaluate each integral:
- [maths rendering]
- [maths rendering]
- [maths rendering]
- [maths rendering]
- [maths rendering]
- [maths rendering]
- [maths rendering]
- [maths rendering]