To integrate the function x^(3/4) + x^(2/3) + x^(1/2) / x dx, we first simplify the expression:
x^(3/4) + x^(2/3) + x^(1/2) / x= x^(3/4) + x^(2/3) + x^(-1/2)
Now we integrate term by term:
∫x^(3/4) dx = (4/7)x^(7/4) + C
∫x^(2/3) dx = (3/5)x^(5/3) + C
∫x^(-1/2) dx = 2x^(1/2) + C
So the final integral of the function is:
(4/7)x^(7/4) + (3/5)x^(5/3) + 2x^(1/2) + C
where C is the constant of integration.
To integrate the function x^(3/4) + x^(2/3) + x^(1/2) / x dx, we first simplify the expression:
x^(3/4) + x^(2/3) + x^(1/2) / x
= x^(3/4) + x^(2/3) + x^(-1/2)
Now we integrate term by term:
∫x^(3/4) dx = (4/7)x^(7/4) + C
∫x^(2/3) dx = (3/5)x^(5/3) + C
∫x^(-1/2) dx = 2x^(1/2) + C
So the final integral of the function is:
(4/7)x^(7/4) + (3/5)x^(5/3) + 2x^(1/2) + C
where C is the constant of integration.