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pie
  • Member for 1 year, 5 months
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  • Egypt
26 votes
Accepted

Evaluate the integral $\int_{-\infty}^{\infty}\binom{n}{x}dx$.

4 votes

$\int_0^{\pi/2}\int_0^{\pi/2}\frac{(\tan\alpha)(\tan\beta)}{\tan\alpha+\tan\beta} d\alpha d\beta=(0.9999999913...)(\pi/2)$? Seriously?

4 votes
Accepted

Conjecture: $\sum\limits_{k=1}^nk^m=S_3(n)\times\frac{P_{m-3}(n)}{N_m}$ for odd $m>1 \ ;\ =S_2(n)\times\frac{P_{m-2}'(n)}{N_m}$ for even $m$.

4 votes
Accepted

Revealing $e$ in real integrals without $e$ or $e^x$ in the integrand

4 votes
Accepted

Compute $\lim\limits_{n\rightarrow+\infty}(\sum\limits_{i=1}^n(1+\frac{i}{n})^i)^{\frac{1}{n}}$

3 votes

How to evaluate $\int\sqrt{\frac{5+x}{7+x}}dx$?

3 votes
Accepted

Does $\int_{e}^{\infty} \frac{1}{x+\ln(x)} \, dx$ diverge or converge?

3 votes

Iterating $\log(x\log(x\log(...)))$

3 votes
Accepted

Integration over an open interval.

3 votes

If $a_1=1$ and $a_{n+1}=3-\frac{1}{a_n}$, show that the sequence converges and find the limit.

3 votes

How to integrate $\int \ln(x+\ln(x+\ln(x+...))) dx$?

3 votes

Show that $\int_{-\infty}^{\infty} \frac{x^2}{\left(x^2+a^2\right)^2} dx = \frac{\pi}{2a}$

2 votes

Sum sequence using Stolzā€“Cesàro

2 votes
Accepted

Doubt on the differentiability of this function over $\mathbb{R}$

2 votes

Integrate $\int \left(\tan x\right)\sqrt{\tan^4x+1}dx$?

2 votes

How can i prove that $n^4-2n^3+2n^2-2n+1$ is not a perfect square?

2 votes

How to evaluate $\int \frac{1}{\sqrt{x^{4}+3x^{2}+2}}dx$?

2 votes

limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$

2 votes

Find the value of the integral: $\int_{0}^{1}\frac{x}{1+x^4}\arctan(x)\,\mathrm{d}x$

2 votes
Accepted

Volume of unit sphere using a single integral

2 votes

How to calculate $\int \sqrt{x^2+x+2} \, dx$?

2 votes
Accepted

How to get the derivative of $\log_4 x$ using the change of base, but without assuming we have the derivative of $\ln x$?

2 votes

Find an upper bound for $\frac{d^{n+1}}{dt^{n+1}} e^{-t} \sin (\frac{\pi t} {2})$

1 vote

how to turn the sum $\lim\limits_{n\to\infty}\left(\prod\limits_{k=0}^n \frac{2n+2k}{2n+2k+1}\right)$ into integral with Riemann sum

1 vote

Limit of $\sqrt x$ as $x$ approaches $0$

1 vote

How to evaluate $\int \frac{1}{x^{2}\sqrt[4]{(x^4+1)^3}} dx$

1 vote

how to solve $\int\frac{\sin(x)-x\cos(x)}{x\sqrt{x\sin(x)}}dx$

1 vote

how to solve $\int \frac{x^2+1}{x^4-x^2+1}dx$

1 vote

What is $\int {\sqrt {1 + 2\sin(x)\cos(x)}dx}$?

1 vote

Evaluting: $\int\frac{1}{(1+\tan x)^2} dx$