Does anyone know how to evaluate #33 or #30?

We use the exponent property

   

so that we can integrate like with any other power function.

question 30

   

let  . then by simple differentiation:

   

performing this substitution:

   

to integrate  u^{-1/2}, add 1 to the exponent then divide by that new exponent.
since -1/2 + 1 = 1/2, change the exponent to 1/2 and divide by 1/2

   



question 33

   

let  . then by simple differentiation:

   

performing this substitution: