anonymous
  • anonymous
How to integrate this...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Picture ? /.\
anonymous
  • anonymous
\[\int\limits (e^{x}+e^{-x})dx\]
anonymous
  • anonymous
oops wait

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anonymous
  • anonymous
That whole expression is over 1.
anonymous
  • anonymous
over... 1?
bahrom7893
  • bahrom7893
do you mean 1 over that whole thing
anonymous
  • anonymous
|dw:1370744044930:dw|
bahrom7893
  • bahrom7893
fmp, can we get the question before your answer?
anonymous
  • anonymous
Well What Do You Believe You Have to Do First ?
anonymous
  • anonymous
|dw:1370744113542:dw|
anonymous
  • anonymous
yeah im sorry I mean 1 on top
anonymous
  • anonymous
|dw:1370744134241:dw|
anonymous
  • anonymous
$$\int\frac1{e^x+e^{-x}}\,\mathrm{d}x=\int\frac{e^x}{(e^x)^2+1}\,\mathrm{d}x=\int\frac1{u^2+1}\,\mathrm{d}u=\arctan u+C=\arctan e^x+C$$
bahrom7893
  • bahrom7893
^finally, someone who can read
anonymous
  • anonymous
Well Wait This Dosn't Make Sense To Me sorry I Don't Think Im Going To Be Much Of Help Hunn @FutureMathProfessor Should Be Able to Help Though ! ^.^
anonymous
  • anonymous
I let \(u=e^x\), and thus \(\mathrm{d}u=e^x\mathrm{d}x\), eliminating the numerator. Then that's just a standard inverse hyperbolic integral.
anonymous
  • anonymous
@oldrin.bataku has it in a succinct fashion
anonymous
  • anonymous
OOPS! inverse trigonometric**
anonymous
  • anonymous
yeah, i was wondering where "hyperbolic" came from
anonymous
  • anonymous
Thanks to all of you that replied!

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