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Math Help - integral - can someone explain this question step by step plz and thank you

  1. #1
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    integral - can someone explain this question step by step plz and thank you

    (x^4+1)^8 4x^3

    i know what the answer is , i just want to see how to do it
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  2. #2
    MHF Contributor arbolis's Avatar
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    Maybe by putting u=x^4+1 and du=4x^3.
    So you have \int u^8 du.
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  3. #3
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    Quote Originally Posted by rock candy View Post
    (x^4+1)^8 4x^3

    i know what the answer is , i just want to see how to do it
     I = \int (x^4+1)^8 \times 4x^3 dx

     \text{Let } u = x^4 + 1

     \text{Then } \frac{du}{dx} = 4x^3

     \therefore du = 4x^3 dx

     \text{Hence } I = \int u^8 du = \frac{u^9}{9} + C = (x^4+1)^9 + C
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  4. #4
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    thanks for clearing that up ... i should of seen that .. i guess im sleepy
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  5. #5
    Super Member redsoxfan325's Avatar
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    It's actually \frac{(x^4+1)^9}{9} + C. You forgot to keep the 9 in the denominator when you subbed back in.
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