Integration by parts – video clips


First take 4 minutes to watch:

That refers to the LIATE rule:

It’s a rule of thumb proposed by Herbert Kasube: whichever function comes first in the following list should be u:

L – Logarithmic functions: ln x, logb x, etc.
I – Inverse trigonometric functions: arctan x, arcsec x, etc.
A – Algebraic functions: x2, 3x50, etc.
T – Trigonometric functions: sin x, tan x, etc.
E – Exponential functions: ex, 19x, etc.

The function which comes lower in the list should be dv.

Functions lower on the list have easier integrals than the functions above them, and functions higher on the list are more likely to produce derivatives simpler than themselves.

It’s not infallible, but it should do for C4.

And then, for a worked example:

And then, for more on calculus from students at Townsend Harris High School in New York: