Reputation
Next tag badge:
95/100 score
19/20 answers
Badges
1 29 82
Impact
~362k people reached

14h
comment Closed-form of $\int_0^1 \frac{\operatorname{Li}_2\left( x \right)}{\sqrt{1-x^2}} \,dx $
VLADIMIR !!!
15h
comment Integrating $\frac{x^3}{\exp(x)-1}$ from $0$ to $\infty$
In general, $$\int_0^\infty\frac{x^n}{e^x-1}~dx~=~n!\cdot\zeta(n+1),$$ and $$\int_0^\infty\frac{x^n}{e^x+1}~dx~=~n!\cdot\eta(n+1).$$ See the Riemann $\zeta$ and Dirichlet $\eta$ functions for more information.
16h
comment Why does $\sqrt{6} + \sqrt{10} + \sqrt{15}$ have four conjugates?
In general, all expressions of the form $(-1)^a\sqrt{p_ip_j}+(-1)^b\sqrt{p_jp_k}+(-1)^c\sqrt{p_kp_i}$ have a minimal polynomial of degree four, where $p_i,p_j,p_k$ are primes.
1d
comment Computing $\sum_{n=-\infty}^\infty \int_{-\pi}^\pi e^{-x^2} \cos(nx) dx $
The answer is $2\pi$.
1d
comment Not the toughest integral, not the easiest one
$I_1=-4\cdot\displaystyle\sum_{n=0}^\infty\frac{\displaystyle{2n\choose n}}{(-4)^n(2n+1)^2}$
1d
answered Use comparison test to determine convergence
1d
comment Solving two diophantine equations.
$(4,41,54,61,64)$ and $(15,47,61,69,73)$
1d
comment Cubic Depressed Form ! What can we deduce form it?
What can we deduce form it ? - That all those sad little cubics are in need of some serious anti-depressants ? :-$($
2d
comment Definite integral: $\int^\pi_0 e^{2a \cos x} \left( \frac{\sin^2 x}{1- \cos x} \right) dx$
@MarcoCantarini: The title and the body of the main post differed originally; see comment.
2d
revised Definite integral: $\int^\pi_0 e^{2a \cos x} \left( \frac{\sin^2 x}{1- \cos x} \right) dx$
added 2 characters in body
2d
answered Antiderivative of $\frac{e^x}{\sqrt{1-x^2}}$
2d
comment Definite integral: $\int^\pi_0 e^{2a \cos x} \left( \frac{\sin^2 x}{1- \cos x} \right) dx$
The title has $a$, and the post has $2a$.
2d
answered Definite integral: $\int^\pi_0 e^{2a \cos x} \left( \frac{\sin^2 x}{1- \cos x} \right) dx$
2d
comment Derivation of Gradshteyn and Ryzhik integral 3.876.1 (in question)
Let $x=a\sinh t$, followed by the trigonometric formula for $\sin A\cos B$, further simplifications, and, ultimately, the integral expressions for Bessel functions.
2d
answered Find $\int_0^1(\ln x)^n\hspace{1mm}dx$
2d
comment Easy method to check integrability as elementary functions
See Liouville's theorem and the Risch algorithm.
2d
comment $i^i$ is real number. But $\ln(i^i)=i\cdot \ln(i)=\frac{i}{2}\ln(-1)$. But $\ln(-1)$ is not defined.
But $\ln(−1)$ is not defined - You sure about that ?
2d
comment logarithmic function?
Zeus Industries bought a computer - Good for them ! Then perhaps they could actually use it, especially since they invested all those money in it, and find out the answer to this question, whose result is ultimately their concern, not mine...
2d
answered Solution for the trignometric equation
Jul
27
comment Integral of an expression involving sine and cosine powers
See also Wallis' integrals and their relation to the beta function.