Whats the step

I wanted to express

$$\large{\displaystyle \int_{0}^{1} \frac{dx}{\sqrt{1+x^{4}}}}$$ in terms of beta function

I started with $$x=\sqrt{\tan t}$$, then got the integral in form of $$sin2t$$ and again substituted $$sin2t=z$$ , after this i couldn't solve

Note by Tanishq Varshney
3 years ago

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I assume you got to this point: $$\displaystyle \frac 1{\sqrt2} \int_0^{\pi /4} (\sin(2t))^{-1/2} \, dt$$,

Now let $$y = 2t$$, you get $$\displaystyle \frac1{2\sqrt2} \int_0^{\pi /2} (\sin(y))^{-1/2} \, dy$$.

Compare with equation 14 and equation 1 from this page.

And apply Euler Reflection Formula, you should get the answer of $$\frac1{8\sqrt\pi} \left [ \Gamma \left( \frac 14\right)^2 \right ]$$.

- 3 years ago

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Thanx for the help $$\ddot \smile$$

- 3 years ago

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- 3 years ago

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Sry couldn't make it in time . Btw are you participating in Proofathon ?

- 3 years ago

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Nope, i am just a beginner to all this , not good as all other members on brilliant

- 3 years ago

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No prob , just give it a try .Btw I am not able to solve 4 questions as of now .

- 3 years ago

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