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    Hi guys, just wondering if anyone could help me with this question, it seems so basic but I can't seem to reach the final answer of 2/3x^3/2 + 4x^1/2 + c

    Integrate x+2 / x^1/2

    I can get the first part of the answer of 2/3x^3/2 , but I can't seem to get the 4x^1/2.

    So sorry if the numbers are horrible to visualize, I have no idea how to post them in picture form like everyone else has!
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    Try differentiating the answer you wish to get and then it will come clear which bit you have failed to integrate initially
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    You fail.

    This is so easy I did it in my head.

    add one to the power and divide by the new power -1/2 + 1 = 1/2 and 2 divided by 1/2 =4

    It's not rocket science.
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    (Original post by Antonton)
    Hi guys, just wondering if anyone could help me with this question, it seems so basic but I can't seem to reach the final answer of 2/3x^3/2 + 4x^1/2 + c

    Integrate x+2 / x^1/2

    I can get the first part of the answer of 2/3x^3/2 , but I can't seem to get the 4x^1/2.

    So sorry if the numbers are horrible to visualize, I have no idea how to post them in picture form like everyone else has!
    Write it as  (x + 2)(x^{-1/2}) Multiply out the brackets and integrate each term.
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    (Original post by Gemini92)
    Write it as  (x + 2)(x^{-1/2}) Multiply out the brackets and integrate each term.
    May I ask, why is it -1/2? I thought when your multiplying by a fraction you "flip" it and multiply, hence 1/ x^1/2 , or is that the same as x^-1/2? Cheers!

    Edit : Oh actually, its indices rule isnt it, the "minus" sign indicates 1 over something, am I right?
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    (Original post by Antonton)
    May I ask, why is it -1/2? I thought when your multiplying by a fraction you "flip" it and multiply, hence 1/ x^1/2 , or is that the same as x^-1/2? Cheers!

    Edit : Oh actually, its indices rule isnt it, the "minus" sign indicates 1 over something, am I right?
    Yes, it's just the fact that x^{-a} = \frac{1}{x^a}
 
 
 
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