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Find an Infinite Series That Converges to the Value Of \int

Question 77

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Find an infinite series that converges to the value of ∫01x2e−x3\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x ^ { 3 } } dx. Is 13−16+118−172…\frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 18 } - \frac { 1 } { 72 } \ldots correct?

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