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Jack Tiger Lam's user avatar
Jack Tiger Lam's user avatar
Jack Tiger Lam's user avatar
Jack Tiger Lam
  • Member for 9 years, 7 months
  • Last seen this week
11 votes

How to compute $\lim_{(x,y) \rightarrow (0,0)} \frac{xy^4}{x^2+y^8}$

10 votes

Antiderivative of $\log(x)$ without Parts

9 votes
Accepted

Prove $\int_0^{\infty}\frac{\ln (x)}{(x^2+1)(x^3+1)}\ dx=-\frac{37}{432}\pi^2$ with real method

9 votes
Accepted

How to show the following integral $\int_0^\frac{\pi}{2} \cot^{-1}{\sqrt{1+\csc{\theta}}}\,\mathrm d\theta =\frac{\pi^2}{12}$

8 votes

The integral of this horrible looking expression

7 votes
Accepted

Evaluation of $ \int \sin (2015x)\cdot \sin^{2013}(x)dx$

6 votes
Accepted

Integrate: $\int \frac{\sin(x)}{9+16\sin(2x)}\,\text{d}x$.

5 votes

Proving $\pi^3 \gt 31$

5 votes
Accepted

Prove $\int_0^2 \frac{\log{x}}{\sqrt{4-x^2}}\text{d}x=0$ without integrating

4 votes

If $A= 2 \cdot \pi/7$ then show that $ \sec A+ \sec 2A+ \sec 4A=-4$

4 votes
Accepted

Quadratic Functional equations.

3 votes

$\frac{1}{1+x^2}+\frac{1}{1+y^2}+\frac{1}{1+xy}≥\frac{3}{1+(\frac{x+y}{2})^2}$ if $x^2+y^2=1$.

3 votes

When does the function $a\cdot \sin(x)+b\cdot \cos(x)-x$ have exactly one real root with multiplicity $1$?

3 votes
Accepted

Integrating $I=\int^{\pi}_0\frac{x}{1-\cos{\beta}\sin{x}}dx$ without Weierstrass Substitution.

2 votes

Computing the value of $\operatorname{Li}_{3}\left(\frac{1}{2} \right) $

2 votes

Evaluate the integral $\int \:\frac{\sqrt{x^2+2x+2}}{x}dx$

2 votes
Accepted

Evaluate: $\int_0^1 \frac{\left(1-x^4\right)^{3/4}}{\left(x^4+1\right)^2} \, dx$

2 votes

Find the limit of the function $f(x,y)=\frac{x^2 y^2}{x^2 y^2 + (x-y)^2}$ whenever $x^2 y^2 + (x-y)^2 \not= 0$ as $(x,y) \to (0,0) $

2 votes

Show that $\left\vert\frac{\pi}{4} - \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9}\right)\right\vert < 0.1$

2 votes

Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$

2 votes

How to calculate $\int_0^1 \frac{1-x}{(x^2-x+1)\log(x)} dx$

2 votes

Evaluate $\lim_{x \to \infty} [(x+2)\tan^{-1}(x+2) -x \tan^{-1}x]$

2 votes

Find the area bounded by a quartic curve

2 votes

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le\frac{3}{\sqrt{7}}$

2 votes

Evaluate $\sum_{k=0}^{511}\frac{\sin\frac\pi{2^{11}}}{\sin\frac{(4k+1)\pi}{2^{12}}\sin\frac{(4k+3)\pi}{2^{12}}}$

1 vote
Accepted

Definite integral (Weierstrass)

1 vote

Solving $\cos x+\sin x-1=0$

1 vote
Accepted

How to Find the Recurrence Formula for $\int \frac{dx} {(1+\sin x)^n}$?

1 vote

find closed form of integal $\int \frac{a e^{-i(a-2)x}}{2(a+2)(1+e^{2ix})}dx$, where $a\in R$

1 vote

Esay way to calculate $\int \frac{1-y^2}{(1+y^2)^2} dy = \frac{y}{1+y^2}+C$