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14h
comment How to find $I=\int_{-4}^4\int_{-3}^3 \int_{-2}^2 \int_{-1}^1 \frac{x_1-x_2+x_3{-}x_4}{x_1+x_2+x_3+x_4} \, dx_1 \, dx_2 \, dx_3 \, dx_4$
Hint: $I=a\ln2+b\ln3+c\ln5$.
14h
answered Evaluate the following integration below
1d
answered How to calculate the integral??
1d
comment Integral of exponencial
$I=\dfrac{\sqrt\pi}a.~$ An obvious first substitution is $t=\sqrt x~,$ since $\big(\sqrt x\big)'=\dfrac1{2\sqrt x}$
1d
comment Is there something interesting about $373857714078$?
$37385771407\color{red}9$ is a prime.
1d
comment Sum of gamma-ish power series
See polylogarithm.
1d
comment If $x=(9+4\sqrt{5})^{48}=[x]+f$ . Find $x(1-f)$.
HInt: The whole idea is to notice that $\big(9-4\sqrt5\big)\big(9+4\sqrt5\big)=1$.
1d
comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
@krvolok: The approach $S=1-S$ definitely belongs to him. He wrote countless volumes, so...
1d
comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
@GFauxPas: Couldn't agree more... The slightly more intuitive explanation is that $\dfrac12$ is the mean between the two extremes, $0$ and $1$, which the partial sums alternately take.
1d
comment How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
@johnmangual: Clearer now ?
1d
revised How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
added 172 characters in body
1d
answered How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
2d
comment Reference for asymptotics on sum
@Michael: Differentiate the sum with regard to a.
2d
comment Find the last two digits of $33^{100}$
@math131: Yes, you are correct. Mathematica confirms the result.
2d
comment Find the roots of equation involving $\arctan x$
@Matan: You should give an interval for the root, based on the observation that $y(a)>0$ and $y(b)<0$ $=>~x_0\in(a,b)$.
2d
answered Find the roots of equation involving $\arctan x$
2d
reviewed Approve Polynomial division in the case of $\frac{x^2 -x}{1-x}$
2d
answered Polynomial division in the case of $\frac{x^2 -x}{1-x}$
2d
comment Find the last two digits of $33^{100}$
@math131: Expand using the binomial theorem, and notice that all terms except the last two are multiples of $100$.
2d
comment Find the last two digits of $33^{100}$
$(-11)^{50}=11^{50}=(10+1)^{50}=\ldots$