Question

integrate (3+x)x^(1/2)dx=?



please help I have no idea how to integrate this problem

Answer 1

just expand the expression

(3+x)x^(1/2) = 3x^(1/2) + x^(3/2)

then just use the power rule on each term.

Answer 2

but with integration there is no power rule wouldn't I have to use substitution?

Answer 3

nope.

Just as

d/dx x^n = n x^(n-1)

∫n x^(n-1) 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)