algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
When I tried to solve this problem, I found a solution (official) video on YouTube. That is a = −b, c = 2024 a = b, c = 2024 and the correct answer is 1 20242025 1 2024 2025. Is there an …
Evaluating $\\int_1^{\\sqrt{2}} \\frac{\\arctan(\\sqrt{2-x^2})}{1+x^2 ...
Dec 30, 2025 · 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, …
calculus - Evaluating $\int_0^1 \frac {\ln (1+x)} { (1+x) (1+x^2 ...
Mar 23, 2025 · Partial fraction decomposition of the integral would lead to, $$\begin {align}\int_0^1 \frac {\ln (1+x)} { (1+x) (1+x^2)} \, dx& = \frac {1} {2}\int_0^1\frac {\ln (1 ...
contest math - Evaluating $4^ {5 \log_ {4\sqrt {2}} (3-\sqrt {6}) - 6 ...
May 9, 2025 · Here's another, seemingly monstrous question from a JEE Advanced preparation book. Evaluate the following expression: $$4^{5 \\log_{4\\sqrt{2}} (3-\\sqrt{6}) - 6\\log ...
calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5}
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 ...
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
The integrand 1 1+x4 1 1 + x 4 is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of 1 1+x4 1 1 + x 4. But I failed to factorize 1 +x4 1 + …
Evaluating $\\lim\\limits_{n\\to\\infty} e^{-n} …
I'm supposed to calculate: $$\\lim_{n\\to\\infty} e^{-n} \\sum_{k=0}^{n} \\frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\\frac{1}{2 ...
Evaluating $\cos (i)$ - Mathematics Stack Exchange
Nov 27, 2020 · Evaluating $\cos (i)$ Ask Question Asked 5 years, 1 month ago Modified 5 years, 1 month ago
Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1/2x}} {x} $$ is equal to: (A) …
calculus - Evaluating $\int_0^1 \sqrt {1 + x ^4 } \, d x ...
Jun 14, 2017 · Throw the command Int[Sqrt[1+x^4],{x,0,1}] to WA, the integral evaluates to $ {}_2F_1 (-\frac12, \frac14; -\frac54; -1 ) \approx 1.0894294132248223224\ldots$ where $ …