30 Noll 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, …

23 Márta 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 ...

2 Iúil 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 ...

11 MFómh 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) …

9 Beal 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 ...

Evaluating ∫ ∞0 ln (x 2 + 1) x 2 + 1 dx Ask Question Asked 12 years, 9 months ago Modified 5 months ago

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 alternative solution but …

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 + x 4. Any …

Inspired by Ramanujan's problem and solution of $\\sqrt{1 + 2\\sqrt{1 + 3\\sqrt{1 + \\ldots}}}$, I decided to attempt evaluating the infinite radical $$ \\sqrt{1 ...

13 MFómh 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?