integration - Evaluating $ \int_ {1/2}^ {\infty} \frac {\Gamma (u ...
4 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 ...
Evaluating $\int_ {-\infty}^ {\infty} \frac {x^6} { (1 + x^4)^2} dx$
Oct 30, 2025 · I am currently stuck on this question and need some help in figuring out where my mistake is. Take complex function $f(z) = \\frac{z^6}{(1 + z^4)^2}$ and integrate ...
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 ...
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 ...
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) …
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 $ \lim\limits_ {n\to\infty} \sum_ {k=1}^ {n^2} \frac {n} {n ...
How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks.
Evaluating $\iiint_B (x^2+y^2+z^2)dV$ where $B$ is the ball of …
The question asks to use spherical coords. My answer is coming out wrong and symbolab is saying I'm evaluating the integrals correctly so my set up must be wrong. Since $\\rho$ is the …
calculus - Evaluating $I=\int_ {0}^ {\frac {\pi} {2}}\prod_ {k=1}^ {7 ...
Oct 23, 2024 · I am attemping to show that $$ I \equiv \int_ {0}^ {\pi/2}\left [\prod_ {k = 1}^ {7}\cos\left (kx\right)\right] {\rm d}x = \frac {\pi} {32} $$ So far I have tried ...