Tolaso's user avatar
Tolaso's user avatar
Tolaso's user avatar
Tolaso
  • Member for 9 years, 4 months
  • Last seen this week
9 votes

Evaluation of $\int\frac{5x^3+3x-1}{(x^3+3x+1)^3}\,dx$

8 votes
Accepted

Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$

8 votes

Show that : $\displaystyle\int_0^{\infty}\frac{\ln(1+x^2)\operatorname{arc\,cot} x}{x}=\frac{π^3}{12}$

7 votes
Accepted

Evaluating the infinite product $ \prod\limits_{n=1}^{\infty} \cos(\frac{y}{2^n}) $

7 votes

How to factorise $x^4 - 3x^3 + 2$, so as to compute the limit of a quotient?

6 votes

General closed form for $L(\phi)=\int_0^\phi \log(\sin x)\mathrm dx$ when $\phi\in(0,\pi)$?

5 votes
Accepted

Interesting Logarithmic Integral: $\int_{0}^{1} \frac{\ln^2 x \ln^2(1+x)}{x} \;dx $

5 votes

Various evalutions of $\int_0^\infty \sin x \sin \sqrt{x} \,dx$

5 votes
Accepted

Evaluate: $\int e^{x^4}(x+x^3+2x^5)e^{x^2} dx$

5 votes
Accepted

How to prove that $\lambda(s)=(1-2^{-s})\zeta(s)$?

5 votes

Find the value of undefinite integral

4 votes
Accepted

Proving Odd & Even Functions

4 votes

Computing $\lim_{A\to\infty} \frac{1}{A} \int\limits_1^A \! A^{\frac{1}{x}} \, \mathrm{d}x.$

4 votes

Evaluate$\int_0^1 \frac{x^{m-1} + x^{n-1}}{(1+x)^{m+n}}dx$ in terms of Beta function

4 votes
Accepted

Closed form for $ \frac{H_k}{k^2} $.

4 votes

What is the value of i^i?

4 votes
Accepted

Need help with $e^x=1/x$

4 votes
Accepted

Is there a closed-form for $\sum_{k=0}^{\infty} \frac{1}{(k!)^2}$?

4 votes
Accepted

Show $\sum \frac{xy}{xy+x+y} \le \frac{6+x^2+y^2+z^2}{9}$

4 votes

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

4 votes

Compute $\int_0^\infty \frac{\ln x}{1+x^2} dx$

3 votes

Evaluate $\lim_{x\rightarrow\mathrm\pi}\frac{\sin(mx)}{\sin(nx)}$

3 votes

Finite sum with inverse binomial

3 votes

The value of following integral

3 votes

$\lim_{h \to 0} \frac{\text{e}^h -1}{h}=1$

3 votes

integration by parts $ \int xe^{-2x} dx$

3 votes
Accepted

Proving $\pi \coth \pi a= \frac{1}{a}+ \sum_{n=1}^{\infty}\frac{2a}{n^2+a^2}$ using the Fourier series for $\cosh ax$

3 votes

A Limit Question of 0/0 Uncertainty

2 votes
Accepted

$n$-th derivative of Beta function

2 votes
Accepted

Are those uses of sum and product notations correct?