Question

integrate x*e^x/sqrt(1+e^x)

Answer 1

Make the substitution that u=sqrt(1+e^x) and you should be able to integrate it :)

Answer 2

oh wait sorry I didn't see the x in front there

Answer 3

\[\int\limits_{?}^{?} {xe ^{x}\over \sqrt{1+e^x}}dx\]]

Answer 4

integrate by parts with u = x and dv/dx = e^x/sqrt(1+e^x)

you then do the above substitution to find v

Answer 5

@eigenschmeigen Final answer:
\[2(x-2)\sqrt{1+e ^{x}}+2{\ln {\sqrt{{1+e ^{x}}}+1\over \sqrt{1+e ^{x}}-1}}+C\]
When I did the substitution you suggested, I didn't get the answer in the book.

Answer 6

\[\int\limits{\frac{e^x}{\sqrt{1+e^x}}}dx \]
let \[u = 1+e^x\]
\[\frac{du}{dx} = e^x\]
\[dx= \frac{du}{e^x}\]
\[\int\limits\limits{\frac{e^x}{\sqrt{1+e^x}}}dx = \int\limits\limits{\frac{e^x}{\sqrt{u}}}\frac{du}{e^x}\]\[=\int\limits\limits\limits{\frac{1}{\sqrt{u}}}du\]

Answer 7

i dont really have time to finish, sorry

Answer 8

@eigenschmeigen That doesn't make any sense!
That integral would give me:\[2\sqrt{1+e ^{x}}+C\]

Answer 9

This was his plan for you:
\[\int\limits_{}^{} x \cdot \frac{e^x}{\sqrt{1+e^x}} dx= x \cdot 2 \sqrt{1+e^x}-\int\limits_{}^{} (x)' 2 \sqrt{1+e^x} dx\]

Answer 10

hint for that one part:
http://openstudy.com/study#/updates/4f7b211ae4b0884e12aafc4b

Answer 11

Ok I will be back on tomorrow if more help is needed
peace

Answer 12

@myininaya I'm not sure where your method progresses to, but an integration by parts plus a trig substitution is too complex. No offense.

Answer 13

I think roadjester's method is a bit easier, but then, myininaya's way is another new thing I learnt today. :)

Answer 14

Sorry, I meant eigenschmeigen's instead of roadjester's.

Answer 15

http://www.wolframalpha.com/input/?i=integrate+%28xe^x%29%2Fsqrt%281%2Be^x%29+dx

Answer 16

yeah, by parts like @myininaya has done, then it requires a trig substitution