user avatar
user avatar
user avatar
Benedict W. J. Irwin
  • Member for 6 years, 2 months
  • Last seen this week
17 votes

Inverse function of a polynomial

15 votes

Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$

14 votes

Is there any meaning to this "Super Derivative" operation I invented?

10 votes

Derivatives 101: what does "with respect to" mean?

8 votes

List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?

7 votes

Integral $\int_{-2}^0 \frac{x}{\sqrt{e^x+(x+2)^2}}dx$

7 votes
Accepted

Find the limiting value of $S=a^{\sqrt{1}}+a^{\sqrt{2}}+a^{\sqrt{3}}+a^{\sqrt{4}}+...$ for $0 \leq a < 1$

5 votes

Inverse of the polylogarithm

5 votes

Known exact values of the $\operatorname{Li}_3$ function

5 votes

Is there a nice general formula for $\int \frac{dx}{x^n-1}$ and/or $\int \frac{dx}{\Phi_n(x)}$?

5 votes
Accepted

On hypergeometric square integral $\int_0^{\infty } \, _2F_1(a,b;c;-x){}^2 \, dx$

4 votes
Accepted

How do you evaluate $\int_0^1 x^n\arcsin^2(x) \, dx$

4 votes

Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

4 votes

Functions with "ugly" inverses

4 votes

Computing the Integral $\int\tanh[b(x-a)]\cos\beta x\,dx$

4 votes

How to integrate $\int\frac{1}{\sqrt{1+x^3}}\mathrm dx$?

4 votes

How can I solve $x^4+x+1=0$ in $\mathbb{C}$?

3 votes
Accepted

Solve $f(t)=1+t-\frac{8}{3}\int ^t_0 (t-\tau)^3f(\tau)d\tau$

3 votes
Accepted

Length Contraction

3 votes

Simpler way to compute a definite integral without resorting to partial fractions?

3 votes

Closed-forms for $\int_0^\infty\frac{dx}{\sqrt[3]{55+\cosh x}}$ and $\int_0^\infty\frac{dx}{\sqrt[3]{45\big(23+4\sqrt{33}\big)+\cosh x}}$

3 votes
Accepted

What is this notation used for combinatorics?

3 votes

Closed Form for the Integral: $\int_0^1 t^n\log\Gamma(t+a)dt$

3 votes

Integral representation of Bessel function K

3 votes

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

3 votes

Is it a coincidence that the $x^2$, and $x^3$ of $\cos$ and sinusoidal integrals relate to Gamma functions?

3 votes

Closed form sought for $a_1 = a_2 = 1, a_n = 1 + \frac{2}{n} \sum_{i=1}^{n-2} a_i $ where $n>2$

3 votes
Accepted

Lagrange Inversion Theorem Proof

3 votes
Accepted

How do I represent this sequence: $ 0,0,1,1,2,2,3,3, \dots$?

3 votes

Closed form for the function $G(x) = \sum_{n=1}^\infty (e^{x/n²}-1) $