Find f(x^(1/2)+4)dx (Where f is the integral sign)

The general form for an integrand if the integral is of the form f(x^n)dx is (1/(n+1)) * x^(n+1) +c This is applied to each term in the question, remembering the constant in the integrand:

So: f(6x+x^(1/2)+4)dx 

=(1/((1/2)+1))*x^((1/2)+1) + (1/(0+1))*x^(0+1) + c

note that 4=4x^0=4*1 as anything to the power of 0 is equal to one- x has an exponent of zero (n=0).

Simplifying terms:

f(6x+x^(1/2)+4)dx = (2/3)x^(3/2) + 4x + c