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Bennett Gardiner's user avatar
Bennett Gardiner's user avatar
Bennett Gardiner's user avatar
Bennett Gardiner
  • Member for 11 years, 1 month
  • Last seen more than a month ago
53 votes

Why learn to solve differential equations when computers can do it?

35 votes
Accepted

How can a function have an antiderivative that can't be written?

28 votes

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

22 votes
Accepted

Evaluating $\int_0^1 \frac{\log x \log \left(1-x^4 \right)}{1+x^2}dx$

21 votes

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

11 votes

Create a Huge Problem

10 votes

How big is a particular n!?

10 votes

Calculate moment of inertia of Koch snowflake

9 votes
Accepted

How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$?

9 votes

How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$

9 votes

The Best of Dover Books (a.k.a the best cheap mathematical texts)

8 votes

Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} - \frac{3}{32\pi^2}.$

7 votes
Accepted

Trigonometric and Exponential Integration

6 votes

Integral $\int_0^{\pi/2} \frac{\sin^3 x\log \sin x}{\sqrt{1+\sin^2 x}}dx=\frac{\ln 2 -1}{4}$

6 votes
Accepted

Solve the equation for $X$

5 votes

Calculate $ \int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx$ where $H(x)$ is a Hermite polynomial

5 votes

How to show $\int^{\infty}_{-\infty}\frac{\sin(ax)}{x(x^2+1)}dx=\pi(1-e^{-a})$? ($a\ge0$)

5 votes

A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$

4 votes
Accepted

Contour integration of log over polynomial with fractional power

4 votes

linear independence question

3 votes
Accepted

Integral $\int_{0}^{\frac{\pi}{4}}\ln\left(\sqrt{\sin^3{x}}+\sqrt{\cos^3{x}}\right)dx $

3 votes
Accepted

Solving $ y'' - y' = -3$ via undetermined coefficients.

3 votes

How to solve differential equation $dy/dx = y^2/(1+y^2)$ by inegration

2 votes
Accepted

Find unique limit for an integral

2 votes

How to express $\log_2 (\sqrt{9} - \sqrt{5})$ in terms of $k=\log_2 (\sqrt{9} + \sqrt{5})$?

2 votes

Does this integral have a closed form?

2 votes
Accepted

Radius of convergence of $\frac{1}{\cosh(z)}$

2 votes

Prove, that $\lim_{x \to \infty} 2^x \sin(\pi/(2^k))$ converges to $\pi$.

2 votes
Accepted

Derivative of Gamma function

2 votes

maximize $\int \limits ^b_a (24 - 2x - x^2)^{1/3}$