Question

How do you find the primitive function of `f(x)=1/sqrt(3-x)` and `f(x)=(4-2x)^-2` ?

Answer 1

You should use different letters for each function. see below.

Explanation:

`u = 3 - x => du = - dx`

`int u^(-1/2) (-du) = - u^(+1/2)/(+1/2) = -2 sqrt {3 - x}`

`v = 4 - 2x => dv = -2 dx`

`int v^(-2) frac{dv}{-2} = -1/2 v^(-1)/(-1) = + frac{1}{2 (4 - 2x)}`