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 \frac ...
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 $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
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 …
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 $\iiint_B (x^2+y^2+z^2)dV$ where $B$ is the ball of radius ...
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 distance from ...
integration - Evaluating $\iiint z (x^2+y^2+z^2)^ {−3/2}\,dx\,dy\,dz ...
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 ...
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 $ \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.
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 ...
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?