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Math Help - Integration (Fraction)

  1. #1
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    Integration (Fraction)

    \int \frac{x}{x+1} \ \mathrm{d}x

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  2. #2
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    Quote Originally Posted by Air View Post
    \int \frac{x}{x+1} \ \mathrm{d}x

    \frac{x}{x+1} = 1 - \frac{1}{x+1}
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by Air View Post
    \int \frac{x}{x+1} \ \mathrm{d}x

    use long division or note that

    \frac{x}{x+1}=\frac{x+1-1}{x+1}=\frac{x+1}{x+1}+\frac{-1}{x+1}=1-\frac{1}{x+1}

    so

    \int \frac{x}{x+1}dx=\int\left( 1-\frac{1}{x+1}\right)dx
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