calc

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



please help I have no idea how to integrate this problem

  • calc -

    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 -

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

  • calc -

    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)

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