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Frank W.

Austin, TX, USA

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24
Evaluating integral $\int_0^1 \frac{x-x^2}{\sin \pi x} dx = \frac{7 \zeta(3)}{\pi^3}$
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23
Infinite sum converging to 2
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13
How can I prove that $\int _{-1}^{1} \frac{1}{x} dx =0 $
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11
Integrating $\frac{\arctan x}{x\sqrt{\smash[b]{1-x^2}}}$
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9
Evaluate $\int_{0}^{\pi} \log \left(m^2-2m\cos x+1\right)\: dx$
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9
Prove that $\displaystyle\int_{0}^{\frac{1}{\sqrt{3}}}\frac{\arctan\left(\frac{1}{\sqrt{1-2x^2}}\right)}{1+x^2} \mathrm{dx}=\frac{13\pi^2}{288}$
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8
How to compute $\zeta'(0)$?
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8
A double sum or a definite integral.
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8
How to compute the integral $\int_0^{\pi/2}\sqrt{\tan(x)} dx$?
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7
$\int(x+1)dx$ yielding different results with $u$-substitution and termwise integration
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7
Integral $\int_0^{\frac{\pi}{2}} x^2 \sqrt{\sin x} \, dx$
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7
A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
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7
Integral for the New Year $2019$!
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7
Closed form for $\int_ 0^{1/2} {\frac {x} {3 +4 x^2}\ln\frac {\ln\left (1/2 +x \right)} {\ln\left (1/2 - x \right)}\mathrm {d} x} $
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7
Evaluating $\int_0^\pi x\frac{\sin{\frac{x}{2}} - \cos{\frac{x}{2}}}{\sqrt{\sin{x}}} dx$
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7
Integrating from $\int_0^\infty \frac{\sin(x)}x dx$ with year $10$ mathematics?
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7
$\Gamma (x) \cos(ax)$ identity
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7
$ \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} = \sqrt[3]{\sqrt[3]{2} -1 } $ for rational $a,b,c$
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6
Integral $I=\int_0^1 \frac{\ln x\arctan(ax)}{1+b^2x^2}dx$
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6
Smart Integration Tricks
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6
integral with parameter and 2 denominators
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6
Evaluate $\sum _{n=0}^{\infty } \frac{16^n}{(2n+1)^3 \binom{2 n}{n}^2}$
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6
Show $\sum\limits_{k=0}^\infty (-1)^k \frac{\Gamma\left(k+\frac14\right)}{\Gamma\left(k+\frac74\right)} = -\Gamma\left(-\frac12\right) = 2\sqrt\pi$
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6
How many methods are there to find $\int_{0}^{\pi} \frac{d \theta}{a+b \cos \theta}, \textrm{ where }a>b>0$
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5
Stuck at this definite integration: $\int_ {0} ^ {\infty} \frac {\log(x)} {x^2 + 2x + 4} \, \mathrm dx$
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5
Evaluate$\int_0^\infty \frac{\log(x)^2}{(1+x)^2}dx$
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5
Evaluate $\int_0^{\pi/2}\ln^2(\sin\theta)\,\mathrm d\theta$
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5
Prove that $\int\limits_{-\infty}^{\infty} \frac{e^{-x}}{1+e^{-2\pi x}}\,dx=\frac1{2\sin\left(\frac{1}{2}\right)}$
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5
How to evaluate the integral $\int_{0}^{1} \frac{\log x}{\sqrt {1+x^2}}dx$
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5
What is $ x^4-7x^3+14x^2-7x+1=0 $?
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