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Math Help - Why am I wrong?!

  1. #1
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    Why am I wrong?!

    \int \frac 4{(1+2x)^3} dx

    =\int 4(1+2x)^{-3}dx

    =\frac {4(1+2x)^{-2}} {-2}

    =-\frac {2}{(1+2x)^2}

    =- \frac {2}{4x^2+4x+1}


    But the model answer is =- \frac {1}{4x^2+4x+1}

    Why did I do wrong?!
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  2. #2
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    Quote Originally Posted by cammywhite View Post
    \int \frac 4{(1+2x)^3} dx

    =\int 4(1+2x)^{-3}dx

    =\frac {4(1+2x)^{-2}} {-2}

    =-\frac {2}{(1+2x)^2}

    =- \frac {2}{4x^2+4x+1}


    But the model answer is =- \frac {1}{4x^2+4x+1}

    Why did I do wrong?!
    \int \! (ax + b)^n \, dx = \frac{1}{a} \cdot \frac{1}{n+1} (ax + b)^{n+1} + C where n \neq -1.

    So you forgot the factor of \frac{1}{a} and you (and the book) forgot the '+ C'.
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