Integration with trig functions

[eaglesfn68]

Homework Statement

integral of x^2/sqrt(9-25x^2)

Homework Equations

The Attempt at a Solution

dont know how to type theta so I am using @

so i made x=3sin@
dx=3cos@d@

sqrt(9-25x^2)=sqrt(9-25(sin^2@))=sqrt(9-225(sin^2@)=sqrt(9(1-25(sin^2@))=sqrt(9(1-25(1-cos^2@))

not sure if I am supposed to make sin^2 into cos^2 -1 or not and not sure were to go next

 

[dextercioby]

You want to have 9-25x^2 = C(1-sin^2 t). What's x(t) and what's C equal to ?

Sin/Cos as substitutions for sqrt(a-bx^2) work equally as well as tanh.