Example 2: Indefinite Integration by Parts

Evaluate ∫ arcsin x dx. A choice of u and dv which works is

u = arcsin x, dv = dx.

We may take v = x. Then

Finally,

arcsin x dx = x arcsin x - (-+ C₍),

arcsin x dx = x arcsin x ++ C.

This integral and the similar formula for ∫ arccos x dx are included in our table at the end of the book. We shall see how to integrate the other inverse trigonometric functions in the next chapter.