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Ben's user avatar
Ben's user avatar
Ben
  • Member for 11 years, 6 months
  • Last seen this week
  • Sydney
45 votes
Accepted

Purely "algebraic" proof of Young's Inequality

37 votes
Accepted

Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$

28 votes

Can $x^3+3x^2+1=0$ be solved using high school methods?

24 votes
Accepted

Draw graph of $\frac{1}{f(x)}$ from graph of $f(x)$

24 votes
Accepted

How to prove :$\lim_{n\to+\infty}\left(\dfrac{u_{n+1}}{u_1.u_2...u_n}\right)^2=2011$

21 votes

Factoring a hard polynomial

11 votes
Accepted

Derivation of the multivariate chain rule

10 votes

Proving AM ≥ GM in 3 variables using the Cauchy-Schwarz inequality

7 votes
Accepted

The roots of $x^3+4x-1=0$ are $a$, $b$, $c$. Find $(a+1)^{-3}+(b+1)^{-3}+(c+1)^{-3}$

7 votes
Accepted

why do we define $\int{e^{-t^2}dt}=\frac{\sqrt{\pi}}{2}erf(t)+c$?

6 votes

How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$

4 votes
Accepted

What is the meaning of | operator?

4 votes
Accepted

What is the notation for a partial factorial?

3 votes

Integrating trigonometric function problem $\int \frac{3\sin x+2\cos x}{2\sin x+3\cos x}dx$

3 votes
Accepted

Proving that $\sqrt{pq} \ne (p + q)/2$ implies $p \ne q$ using the contrapositive

2 votes

Calculus Reduction Formula

2 votes

Computing the Laurent series of $\frac{1}{z^2 + z - 6}$ in the region $2 < |z| < 3$

1 vote

Why does the Laplace transform of $t^2 \exp(at)$ exist?

1 vote
Accepted

Integrating function defined in terms of itself

1 vote
Accepted

Simple Graph Transformation Question $\rightarrow$ $1/f(x)$

1 vote
Accepted

Integration Rule Exact Degree

1 vote

Given positive real numbers $a, b, c$ with $a<b+c$, show that $a/(1+a)<b/(1+b)+c/(1+c)$

0 votes

Identifying the distribution which represents a negative binomial distribution as a compound poisson distribution

0 votes

Finding the derivative of an integral with variable limits: ${\mathrm{d} \over \mathrm{d}x}\int_{x}^{x^2}{1 \over -2y}e^{-5xy^{2}}\mathrm{d}y$?