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Math Help - Can someone please confirm my int. by parts answer?

  1. #1
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    Can someone please confirm my int. by parts answer?

    Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

    Thanks
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by jaijay32 View Post
    Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

    Thanks
    I do not know what is the point of solving it with integration by parts.
    Any way, take u=\sqrt{3x} and dv=xdx
    hence, du=\frac{\frac{3}{2}}{\sqrt{3x}}dx and v=\frac 1 2 x^2

    And apply the formula of integration by parts:
    \int u dv = uv - \int v du .
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jaijay32 View Post
    Hi. I need to integrate x times the square root of 3x. Is integration by parts usable in this case, and if so, can you please work it out (I am not supposed to use the simplification method and the power rule to solve it w/o integration by parts).

    Thanks
    Parts is overkill my friend.

    3x\sqrt{x}=3x^1x^{1/2}=3x^{1+1/2}=3x^{3/2}

    So, take \int3x^{3/2}dx by way of the power rule
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