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Math Help - integration by substitution

  1. #1
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    integration by substitution

    int(cuberoot(x^3+1)x^5dx
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by samdmansam View Post
    int(cuberoot(x^3+1)x^5dx
    please clarify, you are missing some parenthesis. do you mean \int \sqrt[3]{x^3 + 1} \cdot x^5~dx ?
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  3. #3
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    Int by substitution

    Quote Originally Posted by Jhevon View Post
    please clarify, you are missing some parenthesis. do you mean \int \sqrt[3]{x^3 + 1} \cdot x^5~dx ?
    yes thats exactly what I meant, Thanks
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by samdmansam View Post
    yes thats exactly what I meant, Thanks
    ok, well integration by substitution will work nicely. make a substitution of u = x^3 + 1 (and note that x^5 = x^3 \cdot x^2)
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  5. #5
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    Make z^3=x^3+1\implies z^2\,dz=x^2\,dx, it's a more direct way to solve the problem, you get rid of the cube root.
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  6. #6
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    Question could you please take it a little further

    my text has very basic examples then skips to questions with cuberoots
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