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Math Help - Intergal Question

  1. #1
    Super Member
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    Intergal Question

    Hi

    Can someone tell me where my mistake is for the following questions:

    1)Evaluate the integral \frac{e^{x}}{1+e^{2x}}
    u = e^{x}
    u' = e^{x}
    dx = \frac{du}{e^{x}}

    \frac{e^{x}}{1+e^{2x}} * \frac{du}{e^{x}}

    e^{x} cancels so i get:

    \frac{1}{1+e^{2x}} + C
    Not sure if this is correct?

    2)Evaluate the integral \sqrt{1 + \sqrt{x}}
    This is what i have done:

    u = \sqrt{x}
    u' = \frac{1}{2}x^{-0.5}
    dx = \frac{du}{\frac{1}{2}x^{-0.5}}

    final answer i got was \frac{4}{3}x^{\frac{3}{2}} + x^2 + C

    P.S
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  2. #2
    Junior Member slovakiamaths's Avatar
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    for sol.see the attachment
    Attached Files Attached Files
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  3. #3
    Junior Member piglet's Avatar
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    Quote Originally Posted by Paymemoney View Post
    Hi

    Can someone tell me where my mistake is for the following questions:

    1)Evaluate the integral \frac{e^{x}}{1+e^{2x}}
    u = e^{x}
    u' = e^{x}
    dx = \frac{du}{e^{x}}

    \frac{e^{x}}{1+e^{2x}} * \frac{du}{e^{x}}

    e^{x} cancels so i get:

    \frac{1}{1+e^{2x}} + C
    Not sure if this is correct?
    If your going to use substitution, then USE IT. you didn't actually substitute for u in your integral above

     u = e^{x} =>  du = e^{x}dx

    so integral becomes  \int\frac{u}{1+u^{2}}du

    Now integrate with w.r.t. u and fill back in your substitution for u at the end
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  4. #4
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    What does this stand for w.r.t??
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  5. #5
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Paymemoney View Post
    What does this stand for w.r.t??
    with respect to.
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  6. #6
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    thanks guys i found out the solution.
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  7. #7
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