Practice question · Put in order
Order the steps of integration by parts.
- Write down u v minus the integral of v du
- Differentiate u to get du and integrate dv to get v
- Choose u by LIATE and let dv be everything that is left, including dx
- Evaluate the new integral, applying parts again if a polynomial factor remains
- Recognise the integrand as a product of two different types of function
Hints
- You cannot form du and v until u and dv have been assigned.
- The formula is written only once both halves have been processed.
Show the answer
- Recognise the integrand as a product of two different types of function
- Choose u by LIATE and let dv be everything that is left, including dx
- Differentiate u to get du and integrate dv to get v
- Write down u v minus the integral of v du
- Evaluate the new integral, applying parts again if a polynomial factor remains
Why
Parts is bookkeeping: split, differentiate one half, integrate the other, assemble. Repeating the process is normal, each pass lowers the degree of a polynomial factor by one, so needs three passes.
Practise Integration by Parts
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