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, contour integra...
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: $$4^ {5 \log_ {4\sqrt {2}} (3-\sqrt {6}) - 6\log ...
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
Feb 21, 2025 · Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
Evaluating $\cos (i)$ - Mathematics Stack Exchange
Nov 27, 2020 · Evaluating $\cos (i)$ Ask Question Asked 5 years, 1 month ago Modified 5 years, 1 month ago
Evaluating $\int_ {0}^1\int_ {0}^1 xy\sqrt {x^2+y^2}\,dy\,dx$
Calculate the iterated integral: $$\int_ {0}^1\int_ {0}^1 xy\sqrt {x^2+y^2}\,dy\,dx$$ I'm stumped with this problem. Should I do integration by parts with both variables or is there another way to do ...
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
I am trying to evaluate the integral $$\int \frac {1} {1+x^4} \mathrm dx.$$ The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...
Evaluating $\int \cot x \csc^2x \,\mathrm {d}x$ with $u=\cot x$
Also, $\mathrm d\cot (x) = -\csc^2 (x) \mathrm dx$, not $-\cot (x) \csc (x)\mathrm dx$.
calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5} { (x^6+x^3+1 ...
Jul 2, 2025 · The following question is taken from JEE practice set. Evaluate $\displaystyle\int {\frac {x^ {14}+x^ {11}+x^5} {\left (x^6+x^3+1\right)^3}} \, \mathrm dx$. My ...
Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1/2x}} {x} $$ is equal to: (A) $0$ (B) $\frac { …
Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
Sep 13, 2016 · Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?