Does this have a closed form?

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

#Calculus

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Ishan Singh @Pi Han Goh

A Former Brilliant Member - 5 years ago

I seriously doubt it's possible. Why do you think a closed form exists in the first place?

Pi Han Goh - 5 years ago

Because it was asked in an examination :P (the exact way is given in this question)

A Former Brilliant Member - 5 years ago

@A Former Brilliant Member – 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 years ago

@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...

A Former Brilliant Member - 5 years ago

@A Former Brilliant Member – Don't worry about it. There are infinitely many integrals that don't have a closed form.

Pi Han Goh - 5 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$