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Math Help - integral by substitution

  1. #1
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    integral by substitution

    use the substitution u = 2^x to find the exact value of

    integral at the top it says 1 and at the bottom 0 then a fraction :
    top bit = 2^x
    bottom bit = (2^x = 1) squared
    then in the middle at the end it says dx
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  2. #2
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    Quote Originally Posted by cvmsmaths View Post
    use the substitution u = 2^x to find the exact value of

    integral at the top it says 1 and at the bottom 0 then a fraction :
    top bit = 2^x
    bottom bit = (2^x = 1) squared
    then in the middle at the end it says dx
    Do you mean \int_{0}^1 \frac{2^x}{(2^x + 1)^2} \, dx?
    Well then do as it says. Sub u = 2^x \Rightarrow du = 2^x \ln 2 \, dx

    Thus \int_{0}^1 \frac{2^x}{(2^x + 1)^2} \, dx = \frac1{\ln2}\int_{1}^2 \frac1{(u + 1)^2} \, du
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