Newbetuts

Help to evaluate $\int_{0}^{\pi}\sec(x)\sqrt{\tan\left(\frac{x}{2}\right)}\ln^n\tan\left(\frac{x}{2}\right)dx$

Prove that $\lim_{a \to \infty} \sum_{n=1}^{\infty} \frac{(n!)^a}{n^{an}} = 1$.

Prove that $\measuredangle\gamma= 90^{\circ}$

Evaluation of $ \int\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$

Show that if $f$ is continuous on [0,1], then: $\int_0^\frac\pi 2 f(\sin x)dx=\int_0^\frac\pi 2 f(\cos x)dx= \frac12\int_0^\pi f(\sin x)dx$

integrals involving minimum function

How to recognise intuitively which functions grow faster asymptotically?

How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$

Can a function be differentiable at only isolated points?

Infinite Product computation

Simplify recurrence $\frac{d}{dx} f_{n-1}(x)= f_n(x)- f_{n-1}(x) f_1(x)$

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

A divergent series from Futurama

For what $x's$ does $\sum_{k=1}^{\infty} \frac{(k+1)^{k^2}}{k^{k^2+2}} x^k$ converge?

Taking the derivative inside the integral (Liebniz Rule for differentiation under the integral sign)

New posts in calculus

More general Frullani's [closed]

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$

Does $\infty$ mean $+\infty$ in "English mathematics"?

Closed form to an interesting series: $\sum_{n=1}^\infty \frac{1}{1+n^3}$

Integral $\int_0^1(x(1-x))^n\frac{d^n}{d^n x}(\log x \cdot\log (1-x))dx$

Help to evaluate $\int_{0}^{\pi}\sec(x)\sqrt{\tan\left(\frac{x}{2}\right)}\ln^n\tan\left(\frac{x}{2}\right)dx$

Prove that $\lim_{a \to \infty} \sum_{n=1}^{\infty} \frac{(n!)^a}{n^{an}} = 1$.

Prove that $\measuredangle\gamma= 90^{\circ}$

Evaluation of $ \int\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$

Show that if $f$ is continuous on [0,1], then: $\int_0^\frac\pi 2 f(\sin x)dx=\int_0^\frac\pi 2 f(\cos x)dx= \frac12\int_0^\pi f(\sin x)dx$

integrals involving minimum function

How to recognise intuitively which functions grow faster asymptotically?

How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$

Can a function be differentiable at only isolated points?

Infinite Product computation

Simplify recurrence $\frac{d}{dx} f_{n-1}(x)= f_n(x)- f_{n-1}(x) f_1(x)$

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

A divergent series from Futurama

For what $x's$ does $\sum_{k=1}^{\infty} \frac{(k+1)^{k^2}}{k^{k^2+2}} x^k$ converge?

Taking the derivative inside the integral (Liebniz Rule for differentiation under the integral sign)