EXAMPLE 2Use the Table of Integrals to find

x²

564x²

dx.

SOLUTIONIf we look at the section of table titledForms involvinga²-u², we see that the closest entry is number 34.

u²

a²u²

du=u

2

a²u²

+a²

2

sin¹u

a

+C

This is not exactly what we have, but we will be able to use it if we first make the substitutionu=8x.

x²

5-64x²dx=()²

5-²du

8=1

512u²

5-u²du

Then we use Formula 34 witha²=5(soa=

).

x²

5-64x²dx=1

512u²

5-u²du=1

512(-u

2+sin^-1()) +C=-x

+sin^-1() +C