calc
posted by Anonymous .
integrate (3+x)x^(1/2)dx=?
please help I have no idea how to integrate this problem

calc 
Steve
just expand the expression
(3+x)x^(1/2) = 3x^(1/2) + x^(3/2)
then just use the power rule on each term. 
calc 
Anonymous
but with integration there is no power rule wouldn't I have to use substitution?

calc 
Steve
nope.
Just as
d/dx x^n = n x^(n1)
∫n x^(n1) dx = x^n
or, as it is ually written,
∫x^n dx = 1/(n+1) x^(n+1)
So,
∫x^(1/2) dx = 2/3 x^(3/2)
see when you take the derivative of that, that you get x^(1/2)
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