Robert Lee

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15

Integral of the shark function

Sep 11, 2021

15

Find the value of $\displaystyle \int \limits _{0}^{\infty} \dfrac{\mathrm dx}{\sqrt{x^n+a} + \sqrt{x^n+b}}$

Mar 9, 2022

11

What other tricks and techniques can I use in integration?

Apr 26, 2021

8

Let $A=\pi^2\int_{0}^{1}\frac{\sin(\pi x)}{1 + \sin(\pi x)}dx$ and $B=\int_{0}^{\pi}\frac{x\sin( x)}{1 + \sin( x)}dx$. Find $\frac{A}{B}$.

Nov 25, 2021

8

How can I solve this defined integration in an efficient way?

May 11, 2022

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25

How to prove $\int_0^1 \frac{\arctan^2(x)\ln\left(\frac{x}{(1-x)^2}\right)}x \, \mathrm{d}x=G^2$?

Mar 16, 2022

15

How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

Sep 17, 2021

13

How to show $ \int_{-\infty}^{\infty} \frac{e^{-(x+1)^2}}{1+e^{-x}}\mathrm{d}x = \frac{\left(2\sqrt[4]{e} -1 \right)\sqrt{\pi}}{2e}$?

Sep 25, 2022

12

Find matrix $A\in \mathcal{M}_n (\mathbb{N})$ such that $A^k =\left( \sum_{i=1}^{k}10^{i-1} \right)A$.

Sep 27, 2020

10

How can I prove that these definitions of curl are equivalent?

Jul 13, 2020

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integration

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Generate Functions/Formulae From Graph

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Calculate $\int_0^\infty \frac{\sin\left(x^2 - \arctan\left(\frac{1}{x^2}\right)\right)}{\sqrt{1 + x^4}} \, dx $

+10

How to show $ \int_{-\infty}^{\infty} \frac{e^{-(x+1)^2}}{1+e^{-x}}\mathrm{d}x = \frac{\left(2\sqrt[4]{e} -1 \right)\sqrt{\pi}}{2e}$?

+10

How to show $ \int_{-\infty}^{\infty} \frac{e^{-(x+1)^2}}{1+e^{-x}}\mathrm{d}x = \frac{\left(2\sqrt[4]{e} -1 \right)\sqrt{\pi}}{2e}$?

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