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: $$4^ {5 \log_ {4\sqrt {2}} (3-\sqrt {6}) - 6\log ...
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
Feb 21, 2025 · Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
I am trying to evaluate the integral $$\int \frac {1} {1+x^4} \mathrm dx.$$ The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...
Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the complex p...
calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5} { (x^6+x^3+1 ...
Jul 2, 2025 · The following question is taken from JEE practice set. Evaluate $\displaystyle\int {\frac {x^ {14}+x^ {11}+x^5} {\left (x^6+x^3+1\right)^3}} \, \mathrm dx$. My ...
Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
Sep 13, 2016 · Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?
Evaluating $\\lim_{n\\to\\infty}\\left( \\frac{\\cos\\frac{\\pi}{2n ...
Jan 24, 2025 · Since the OP solve his/her problem, I just as well complete the solution: \begin {align} \frac {1} {n+1}\sum^n_ {k=1}\cos\left (\tfrac {k\pi} {2n}\right)&=\frac {n ...
Evaluating $\int_ {0}^1\int_ {0}^1 xy\sqrt {x^2+y^2}\,dy\,dx$
Calculate the iterated integral: $$\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 ...
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