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Thread: Why is my evaluation of this integral wrong?

  1. #1
    s3a
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    Why is my evaluation of this integral wrong?

    My work is attached and any input would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Why is my evaluation of this integral wrong?-mywork.jpg  
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  2. #2
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    algebra, algebra, algebra ...

    u^2+25 \ne (u-5)(u+5)


    \int \frac{e^{4x}}{e^{8x} + 25} \, dx <br />

    u =e^{4x}

    du = 4e^{4x} \, dx

    \frac{1}{4} \int \frac{4e^{4x}}{e^{8x} + 25} \, dx

    \frac{1}{4} \int \frac{du}{u^2 + 25} \, dx

    \frac{1}{20} \arctan\left(\frac{u}{5}\right) + C<br />

    \frac{1}{20} \arctan\left(\frac{e^{4x}}{5}\right) + C
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  3. #3
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by skeeter View Post
    algebra, algebra, algebra ...

    u^2+25 \ne (u-5)(u+5)


    \int \frac{e^{4x}}{e^{8x} + 25} \, dx <br />

    u =e^{4x}

    du = 4e^{4x} \, dx

    \frac{1}{4} \int \frac{4e^{4x}}{e^{8x} + 25} \, dx

    \frac{1}{4} \int \frac{du}{u^2 + 25} \, dx

    \frac{1}{20} \arctan\left(\frac{u}{5}\right) + C<br />

    \frac{1}{20} \arctan\left(\frac{e^{4x}}{5}\right) + C
    How on god's green earth could you read that sheet!? :0
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  4. #4
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    Quote Originally Posted by AllanCuz View Post
    How on god's green earth could you read that sheet!? :0
    I decipher hieroglyphs in my spare time ...
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  5. #5
    s3a
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    Oh ya! I always make that mistake when I do things fast. Thanks! (and lol sorry for my handwriting)
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