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Integral help, how to approach this?

Mathematics
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\[\int\limits_{0}^{1} \sin(y)(e-e^{y^{1/3} })dy\] is the integral. I can plug it into wolfram alpha and get a value, but I would like to know what steps get me there>
Wow. That's an interesting integral. I would suggest distributing the sine function across and take the integral sepearately. e is constant so you can just factor that out. For the second integral, it gets a bit difficult. You could try and work with integration by parts twice.
Except that the product of siny and e^y^1/3 is elliptic. Neither of those will differentiate to zero.

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Heh, I have a whole homework sheet of these iterated integrals that the inner integral isnt bad, but the insides are just impossible. WA wont even give steps, just values when I include the bounds.. Arg
That is one hairy integral!
have you tried considering y^(1/3) as u ?
I don't think you can use u-sub, since you don't have a du to substitute. But, I think since the integral is from 0
i would use taylor series to solve this problem
Not series to solve the whole integral! Omg.
i used taylor's expansion and i got 0.1644
unless u want to use integration by parts and the Jacobin and polar coordinate,
to solve this problem
Well, depending on the course this is being taught in, which is probably a Calc BC (II) course, I would suggest parts. However, if this was for ODE, then I might suggest using poolar coordinates or series expansion.

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