# Integral of $\int\limits_0^1\frac{1}{1+x ^\frac{\pi}{2}}dx$ [closed]

How do I calculate the integral

$$I=\int\limits_0^1\frac{1}{1+x^\frac{\pi}{2}}dx$$

I have no idea about the gamma and beta function. In the comments it has been proposed to use gamma and beta functions. how can I go about doing it especially the use of gamma and beta functions.

## closed as off-topic by Jack D'AurizioJun 15 '18 at 16:46

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• Do you mean $$\int\frac{1}{(1+x)^{\pi/2}}dx$$? – Dr. Sonnhard Graubner Jun 15 '18 at 16:44
• Are you able to solve $\int \frac {dx}{x^{\alpha}}$? – lulu Jun 15 '18 at 16:45
• Use $x=\tan^{4/\pi}t$ and some basic facts about the Beta and Gamma functions. – J.G. Jun 19 '18 at 6:27
• The closed form of this involves polygamma functions. It is highly unlikely that the average evaluator of integrals is going to know about them – graveolensa Aug 29 '18 at 14:26
• $\int_{0}^{1} \frac{dx}{1+x^{\pi/2}}=\frac{\psi ^{(0)}\left(\frac{1}{2}+\frac{1}{\pi }\right)-\psi^{(0)}\left(\frac{1}{\pi }\right)}{\pi }$ where $\psi$ is the polygamma function. See my earlier question math.stackexchange.com/questions/42093/… – graveolensa Aug 30 '18 at 21:34