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Does this have a closed form?

Does the following expression have a closed form? \[\int_0^{\frac{\pi}{2}} x^{\sin x + \cos x} \, dx\]

Note by Deeparaj Bhat
5 months, 3 weeks ago

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@Ishan Singh @Pi Han Goh Deeparaj Bhat · 5 months, 3 weeks ago

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@Deeparaj Bhat I seriously doubt it's possible. Why do you think a closed form exists in the first place? Pi Han Goh · 5 months, 3 weeks ago

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@Pi Han Goh Because it was asked in an examination :P (the exact way is given in this question) Deeparaj Bhat · 5 months, 3 weeks ago

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@Deeparaj Bhat The point of that question is to find the integer part of the numerical value of that integral, not the exact form of the integral. Pi Han Goh · 5 months, 3 weeks ago

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@Pi Han Goh I know. But many times, they give stuff whose closed form can be found using out of syllabus stuff but we're expected to get bounds via elementary methods. So, I was curious... Deeparaj Bhat · 5 months, 3 weeks ago

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@Deeparaj Bhat Don't worry about it. There are infinitely many integrals that don't have a closed form. Pi Han Goh · 5 months, 3 weeks ago

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