Practice question · Sort into groups
Sort each integral by which factor LIATE tells you to take as u.
Groups: Take u = the polynomial part · Take u = the logarithm
- x^2 e^x dx
- x cos x dx
- x^2 ln x dx
- x ln x dx
- x e^x dx
Hints
- Read the LIATE list from the left and take the first type that appears in the integrand.
- Logarithmic sits before Algebraic, which sits before Trigonometric and Exponential.
Show the answer
Take u = the polynomial part: x e^x dx, x cos x dx, x^2 e^x dx
Take u = the logarithm: x ln x dx, x^2 ln x dx
Why
Whenever a logarithm is present it wins, because ln x has no elementary antiderivative you would want as v but differentiates to a tidy 1/x. Against exponentials and trig functions the polynomial wins, since differentiating it drives the degree down to zero.
Practise Integration by Parts
The app has 6 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
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