They just keep getting more complex, help! Find the indefinite integral: Integrand of ((xe^(-x^2))+(e^x)/((e^x)+8))
i don't even know where to begin!
I would do one part at a time. Can you find \[\int\limits xe^{-x^2} dx\]yourself?
um... u=(-x^2), du=-2x?
looks good so far.
so that part would be 1/2(e^(-x^2)+c?
Put a negative in front, but otherwise, looks great.
oh yeah..
how do i determine u, for the second part - would it be (e^x)+8?
That looks like the u that I would would use.
now for du.. would it be just e^x?
or actually be 1/(e^x)?
Just \(e^x\)
ok from there, would my substitution for the second part be: Integrand of du(u^-1)?
and then just add them together as a final answer?
Integrate\[\int\limits {1 \over u}\;\;du\]substitute the u back in, add them together, and put a little +C at the end.
so the second part would = e^x(e^x+8)
and add it to the first part.. hmmm
I'm getting a different solution for the second part. What's the integral of \(1\over u\)?
oh, sorry. Actually it should be ln |u|?
yup. But since \(e^x+8>0\), you can drop the absolute value once you substitute back in for x.
got it! I guess i get confused as to when I need to stop taking the derivative.. lol
nice job.
thank you!
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