Evaluating Blockchain Startups Navigating The Crypto Vc Funding

4 days ago · For more details on how to carry out the methods suggested by the two answers here (currently), see the answers to: How to integrate $ \int \frac {x} {\sqrt {x^4+10x^2-96x …

5 days ago · I was recently trying to compute the value of the integral $$\int_1^ {\sqrt {2}} \frac {\arctan (\sqrt {2-x^2})} {1+x^2}\,\mathrm dx.$$ I’ve tried differentiation under the integral sign, …

Dec 13, 2025 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

Dec 26, 2025 · $$ I_n=\int_ {1}^ {\infty}\frac {n\bigl (x^ {\alpha+1}-x^\alpha\bigr)\sin\!\left (\frac {1} {x}-1\right)} {x^3\bigl (x^\alpha+n^\alpha (x-1)^\alpha\bigr)}\,dx, \qquad ...

Dec 9, 2025 · Is there a closed-form expression for the series $$ \\sum_{k=0}^n\\binom\\alpha k^2\\lambda^k,\\quad \\alpha ~ \\text{is non-integer} $$ There is an identity involving binomial …

Jul 2, 2025 · The following question is taken from JEE practice set. Evaluate $\displaystyle\int {\frac {x^ {14}+x^ {11}+x^5} {\left (x^6+x^3+1\right)^3}} \, \mathrm dx$. My ...

I am trying to evaluate the integral $$\int \frac {1} {1+x^4} \mathrm dx.$$ The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...

Nov 11, 2025 · I am evaluating the following integral: $$\\int_0^{1} \\left(\\tanh^{-1}(x) + \\tan^{-1}(x)\\right)^2 \\; dx$$ After using the Taylor series of the two functions, we ...

Also, $\mathrm d\cot (x) = -\csc^2 (x) \mathrm dx$, not $-\cot (x) \csc (x)\mathrm dx$.

Oct 23, 2024 · I am attemping to show that $$ I \equiv \int_ {0}^ {\pi/2}\left [\prod_ {k = 1}^ {7}\cos\left (kx\right)\right] {\rm d}x = \frac {\pi} {32} $$ So far I have tried ...