Mhenni Benghorbal

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739 Answers

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32
Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$
32
please solve a 2013 th derivative question?
15
Evaluate the integral $\int_0^{\infty} \left(\frac{\log x \arctan x}{x}\right)^2 \ dx$
13
How to solve this recurrence relation? $f_n = 3f_{n-1} + 12(-1)^n$
11
Compact formula for $\sum_k k!$
11
How to determine equation for $\sum_{k=1}^n k^3$
11
$\int_{0}^{\infty} \frac{\cos x - e^{-x^2}}{x} \ dx$ Evaluate Integral
10
How to show that $f(x)=x^2$ is continuous at $x=1$?
9
How to integrate, $\int_{0}^{\pi/2}\sin (\tan\theta) \mathrm{d\theta}$?
8
A nonlinear “Fredholm” integral equation
8
Find all complex numbers satisfying the equation.
7
Methods to evaluate $ \int _{a }^{b }\!{\frac {\ln \left( tx + u \right) }{m{x}^{2}+nx +p}}{dx} $
7
half-derivative of $x^2$
7
Why is $\log(\sqrt{x^2+1}+x)$ odd?
7
$\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
6
$\int_0^{\infty}\frac{\ln x}{x^2+a^2}\mathrm{d}x$ Evaluate Integral
6
Simple equivalent of $\sum\limits_{i=1}^N\frac{\log i}i$
6
Convergence/Divergence of $\int_{0}^{1/e} \frac{\log \left(\frac{1}{x}\right)}{(\log^2 (x)-1)^{3/2}} \mathrm{dx}$
6
Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
5
$\int_0^1 \sqrt {\tan^{-1}x}\space dx=$?
5
How to find the limit of $\dfrac{\ln(\ln(\frac{n}{n-1}))}{\ln(n)}$?
5
When is $\frac{2^n+1}{n^2}$ an integer?
5
Evaluate : $\int_0^1 \frac{dx}{\sqrt[3]{1-x^3}}$.
5
Prove: $\int_0^1 \frac{\ln x }{x-1}=\sum_1^\infty \frac{1}{n^2}$
5
Bessel and cosine function identity formula
5
Compute using Complex Analysis: integral
5
The double integral $\int_0^1 \int_0^1 \frac{1-x}{1-xy}(-\log(xy))^s \, dx \, dy$
5
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
5
How to evaluate this rational limit
5
Algorithms for “solving” $\sqrt{2}$
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