integration - Evaluating $ \int_ {1/2}^ {\infty} \frac {\Gamma (u ...
5 days ago · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, …
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 ...
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?
integration - Evaluating $\sum_ {m=0}^\infty \sum_ {n=0}^\infty …
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 ...
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) …
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?
integration - Evaluating $\iiint z (x^2+y^2+z^2)
Jul 29, 2020 · Spherical Coordinate Homework Question Evaluate the triple integral of $f (x,y,z)=z (x^2+y^2+z^2)^ {−3/2}$ over the part of the ball $x^2+y^2+z^2\le 81$ defined by ...
complex numbers - Evaluating $\cos (i)$ - Mathematics Stack …
Nov 27, 2020 · Others answered about how cos(i) c o s (i) can be calculated using Euler's formula. But I will elaborate from a different perspective. We know that cosine function can be …
Evaluating $\int_0^\pi x\frac {\sin {\frac {x} {2}} - \cos {\frac {x ...
Aug 14, 2022 · This definite integral is solved if the minus sign is replaced by a plus sign, and it yields $\pi^2$. $$ \mathcal {I} = \int_0^\pi x \cdot \frac {\sin {\frac {x} {2 ...
integration - Evaluating $\int_ {0}^ {2\pi}\cos ^2 (x)\sin (x) \ dx ...
Jun 3, 2024 · The answer is correct, and the approach is correct in general, but notation-wise, you have not changed the bounds of the integral after substitution. The integral should change to …