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 $\int \frac {1} { {x^4+1}} dx$ - 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 + …
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 $\iiint_B (x^2+y^2+z^2)dV$ 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 …
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 ...
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 $ \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?