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Mathematics
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Bob Dobbs
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View all questions and answers
answer
14
How to calculate $\int_{0}^{\infty}\frac{x^{2}\ln x}{(1+x^{3})^4}dx$
Apr 14, 2023
question
12
Show: $4\pi=\int_0^{\frac\pi2}\int_0^{\frac\pi2}\frac{4+2\sin^2\phi\sin^2\theta}{\left(1-\frac14\sin^2\phi\sin^2\theta\right)^{\frac32}}d\theta d\phi$
May 30
answer
12
How do we evaluate this REALLY tricky integral $\int{\frac{\cos 9x + \cos 6x}{2 \cos 5x-1} dx}$
Mar 31, 2023
answer
10
What type of topological space is this?
Dec 4, 2023
answer
7
Easiest way to evaluate $\int_0^{\pi/6}\sec x\,dx$?
Jul 12, 2022
answer
7
Evaluate $\sum_{n\geq 0} \mbox{arccot}(n^2 + n + 1)$
Nov 2, 2022
question
7
How to prove $\sum_{k=1}^n{n\choose k}\frac{(-1)^{k+1}}{k}=\sum_{k=1}^n\frac{1}{k}$?
Jan 8, 2023
question
7
Show that $\int_0^{\frac{\pi}2}K(\sin t)dt=\frac{\Gamma(\tfrac14)^4}{16\pi}$
Feb 21, 2024
answer
7
$|\sin\phi_{n}(x)| = \sqrt{\frac{1}{2} - \dfrac{1}{2[1+ (\omega_{n}a(x))^{2}]^{1/2}}}$
Sep 27, 2022
answer
7
Compute $ \lim_{ x \to a } \frac{x^x-x^a}{x-a} $ without L'Hopital's rule
Nov 15, 2024