Page 13 - Calculus for the Clueless

Example 14—

Crazy exponent: u - In x; du = (1/x)
dx.

Example 15—

Crazy exponent (only real choice) plus trig identity: u = sin x; du = cos x dx = dx/sec x.

Example 16—

One of my favorites. This one looks exactly like the one in Example 16A but is really different:
4x
4x
u = e + 1; du = 4e dx.

Inverse Trig Functions

This part is the last of the basic integrals that you must know by sight. In some schools, all six inverse trig
functions must be known; in some, you learn three; and in some, like in my school, you learn two. We will do
three—arc sin, arc tan, arc sec.

Rule 5