Practice question · Select all that apply
Select every integral that integration by parts handles well rather than substitution.
Hints
- Check first whether an inner function's derivative is sitting in the integrand.
- If a substitution closes the integral immediately, parts is the wrong tool.
Show the answer
- B. x^2 e^x dx
- C. x sin x dx
- D. ln x dx
Why
Options 3 and 5 are pure substitutions ( and , with the inner derivative present). The other three are products of unrelated types — including the lone ln x, taken with dv = dx — and belong to parts.
Practise Integration by Parts
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