anonymous
  • anonymous
integration of (1+e^x)^2 /e^x
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
expand the top, divide out the denominator and see what we got left?
anonymous
  • anonymous
\[\int\limits_{a}^{b} ((1+e^x)^2)/e^x \] hmmm... long time since Cal II. Maybe Integration by Parts?
anonymous
  • anonymous
\[\int \left(e^{-x} + e^{x} + 1 \right)dx = -e^{-x} + e^x + x \]

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amistre64
  • amistre64
\[\int\frac{(1+e^x)^2}{e^x}dx\] \[\int\frac{1+2e^x+e^{2x}}{e^x}dx\] \[\int\frac{1}{e^x}+\frac{2e^x}{e^x}+\frac{e^{2x}}{e^x}dx\] \[\int e^{-x}+{2e^x}+{e^x}dx\]
amistre64
  • amistre64
typoed myself lol
amistre64
  • amistre64
\[\int e^{-x}+2+{e^x}dx\] as i see it
anonymous
  • anonymous
yup it should be 2 sorry my bad ..amistre is right
anonymous
  • anonymous
Whoops I made a mistake.
amistre64
  • amistre64
my brain did it right, and my fingers argued with me lol
anonymous
  • anonymous
so the final answer is \[-e^-x+2x+e^x ?\]

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