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I have to solve $\int_0^1 y^7 e^{xy^4} \mathrm{d}y$ by using Fubini's theorem. My idea was to rewrite $y^7 e^{xy^4}$ as $\int_0^x f(t) \mathrm{d}t$, but I cannot figure out the term for $f$. I currently have $\int_0^x y^{11} e^{ty^4} \mathrm{d}t = y^7e^{xy^4}-y^7$.

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  • $\begingroup$ $\int _0^x y^{11}e^{ty}dt = y^{10} (e^{xy} - 1)$ $\endgroup$ – Alvin Lepik Jul 13 '19 at 16:08
  • $\begingroup$ What Fubini theorem do you use for single integrals? Can you state the theorem? $\endgroup$ – Zacky Jul 13 '19 at 17:04
  • $\begingroup$ What I think the idea behind the task is, is that in the end you have $\int_0^1 \int_0^x f(t) dt dy = \int_0^x \int_0^1 f(t) dy dt$. $\endgroup$ – Tim Jul 13 '19 at 17:09

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